# A Fixed Point Theorem For Contractions Of Rational Type In Partially Ordered Metric Spaces

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### Fixed Point Theorems for Generalized -Contraction Type Maps

Keywords: Fixed point, Contractive map, -contraction type map 1 Introduction and preliminaries Jaggi [10] obtained a generalization of the Banach s contraction principle by introducing the notion of rational type contractive condition. Harjani et al. [8] extended the result of Jaggi [10] to the case of partially ordered metric.

### FIXED POINT THEORY IN TERMS OF A METRIC AND OF AN ORDER RELATION

[11] A. Amini-Harandi, H. Emami, A xed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary di erential equations, Nonlinear Analysis: Theory, Methods & Appl., 72(2010), 2238-2242.

### FIXED POINTS OF φ - ALMOST GENERALIZED WEAKLY CONTRACTIVE

of partially ordered metric spaces. Theorem 2.2. [17] Let (X;≼;d) be a partially ordered complete metric space. Let T: X! Xbe a continuous and non-decreasing mapping such that the inequality (2.1) is satis ed for all x;yin Xwith x≼ y. If there exists x0 in Xwith x0 ≼ Tx0 then T has a xed point. Theorem 2.3. [17]

### J. Adv. Math. Stud. Vol. 10(2017), No. 1, 74-83

[8] S. Chandok and J.K. Kim: Fixed point theorem in ordered metric spaces for generalized contractions mappings satisfying rational type expressions, NonlinearFunct. Anal.Appl.,17(2012), 301-306. [9] S. Chandok, B.S. Choudhury and N. Metiya: Some ﬁxed point results in ordered metric spaces for

### RESEARCH Open Access Fixed point theorem for generalized weak

In this paper, we prove a fixed point theorem for generalized weak contractions satisfying rational expressions in partially ordered metric spaces. The result is a generalization of a recent result of Harjani et al. (Abstr. Appl. Anal, Vol.2010, 1-8, 2010). An example is also given to show that our result is a proper generalization of the

### Suzuki Type Common Fixed Point Theorem For Four Maps Using

[20] S.Chandok and D.Kumar,Some common fixed point results for rational type contraction mappings in complex valued metric spaces,Journal of Operators,2013,6 pages, Article ID 813707. [21] S.L.Singh,H.K.Pathak , S.N.Mishra,On a Suzuki type general fixed point theorems with applications,Fixed Point Theory Appl.,2010,(2010),15 pages,Article ID

### F A S C I C U L I M A T H E M A T I C I

A FIXED POINT THEOREM FOR CONTRACTIVE MAPPINGS WITH NONLINEAR COMBINATIONS OF RATIONAL EXPRESSIONS IN b-METRIC SPACES Abstract. In this paper we discuss the existence and uniqueness of xed points for mappings satisfying several (nonlinear-combi-nations) contractive inequalities of rational type controlled by al-tering distance functions.

### Research Article Fixed Point Results Satisfying Rational Type

conditions satisfying rational type expressions in partially ordered metric spaces. Mustafa et al. [] discussed xed point results by almost generalized contraction via rational type expression which generalizes, extends, and unies the resultsofJaggi[ ],Harjanietal.[ ],andLuongandu an [ ], respectively. Fixed point theorems for contractive type

### COUPLED FIXED POINT THEOREM FOR RATIONAL CONTRACTION

non-linear contractions in partially ordered metric spaces. Furthermore, after the work of Bhaskar and Lakshmikantham [7] coupled ﬁxed point theorems have been established by many authors in different type of spaces (see [8,9,10]). In this paper, we have establish a coupled ﬁxed point theorem satisfying rational contraction

### Fixed Point Results for Rational type contraction in

Fixed Point Results for Rational type contraction in Partially ordered Complex Valued Metric Spaces Binayak S. Choudhury, Nikhilesh Metiya, and Pulak Konar Abstract. In this paper we present some results of xed point theory in a recently introduced generalization of the metric space, that is, complex valued

### Др Бошко Дамјановић редовни професор ОБРАЗОВАЊЕ И УСАВРШАВАЊА

6. Common Coupled Fixed Point Ttheorem for Geraghty-Type C contraction in Partially Ordered m metric Spaces, Liu Xiao-lan, Zhou Mi, Damjanovic Bosko,2018,Journal of function spaces, M21a 7. Fixed point results on θ-metric spaces via simulation functions,Chanda, A., Damjanović, B., Dey, L.K., 2017, Filomat, M22 8. Ulam-Hyers stability, well

### Coupled Fixed Point Theorem and Dislocated Quasi -Metric Space

coupled fixed point theorems have been established by many authorsin different type of spaces (see [ 2, 4, 6]). In this paper, we establish a coupled fixed point theorem satisfying contraction conditions in the context of dislocated quasi -metric space. An example is given in the support of our main results. Definition[ 11 ].

### Fixed points for -Suzuki contractions with applications to

[31]Paesano, D. and Vetro, P., Suzuki s type characterizations of completeness for partial metric spaces and ﬁxed points for partially ordered metric spaces, Topology Appl., 159 (2012), 911 920 [32]Ran, A. C. M. and Reurings, M. C., A ﬁxed point theorem in partially ordered sets and some applications to matrix

### Angel Almeida, Antonio-Francisco Roldan-Lopez-de-Hie ´ rro

a practical point of view, it is convenient that these contractivity conditions are symmetric. This paper has two main purposes: as ﬁrst objective, we present a general-ization of Theorems 1, 2 and 3 by using diﬀerent kinds of control functions both in the setting of metric spaces and in the framework of partially ordered metric spaces.

### Review Article - A study of some fixed point theorems for

coincidence point theorem in partially ordered metric spaces with an implicit relation. Fixed Point Theory Appl. 2013, mappings. 38: 11. [37] [11] Hitzler, P. and Seda, A. K. (1999). Multi-valued mappings, fixed point theorems and disjunctive databases. 3rd Irish Workshop on Formal Methods (IWFM-99), EWIC, British Computer Society.

### INTERNATIONAL CONFERENCE ON FIXED POINT THEORY AND ITS

Multivalued and singlevalued common fixed point results in partially ordered metric space (AP) Dorel Mihe. ţ. Probabilistic contractions with applications in the stability of functional equations. 19.30 Departure by bus to URSUS Beer Factory (in front of the main building of the University)

### Fixed points of generalized -Meir-Keeler type contractions

b-metric-like space as well as in a partially ordered b-metric-like space. In this work, by using the concepts of Meir-Keeler contractions, -admissible mappings, and b-metric-like spaces, we de ne the concept of generalized -Meir-Keeler contraction mappings in b-metric-like spaces. Then we investigate some xed point results for these

### Fixed point theorems for multivalued generalized contractions

A ﬁxed point theorem for contractions of rational type in partially ordered metric spaces, Annali dell Universita di Ferrara, DOI 10.1007/s11565-013-0176-x [2]Hu, S. and Papageorgiou, N. S., Handbook of Multivalued Analysis, Vol.

### Unique fixed point theorems in partially ordered metric spaces

Unique ﬁxed point theorems in partially ordered metric spaces N.SeshagiriRaoa,

### COUPLED FIXED POINT THEOREM FOR MULTI-VALUED MAPPING VIA

theorems for generalized non-linear contraction in partially ordered metric spaces. In the concerned work, using the idea of generalized rational type contraction condition, coupled xed point theorem for multi-valued hybrid maps in the structure of complete partially ordered metric spaces have been investigated. De nition 1.1.

### TABLE OF CONTENTS, JOURNAL OF COMPUTATIONAL ANALYSIS AND

Weighted composition operators from Zygmund-type spaces to weighted-type spaces, Yanhua rational type contractions in partially ordered S-metric spaces, Mi

### Fixed Point Theorems for Quadruple Self-Mappings Satisfying

in partially ordered metric spaces and has given the applications of their results. Shatanawi [19], proved coupled ﬁxed point theorems in partially ordered metric spaces for two altering distance functions. Nadler [26] worked on the ﬁxed point theorem for multivalued contraction mappings. Branciari [27]

### A Common Coupled Fixed Point Theorem in Complex Valued Metric

fixed point theorems for rational contractions in partially [5] Azam A, Ahmad J, Kuman P (2013), Common fixed point theorems for multi-valued mappings in complex-valued metric spaces, J. Inequal. Appl., Article ID 578. [6] Azam A, Fisher B, Khan M (2011), Common fixed point theorems in complex valued metric spaces, Numerical

### Fixed Point Theorems of 𝐋𝐖 -Type Lipschitz Cyclic Mappings in

theorem of fixed point of a contractive mapping in metric spaces that is Banach contraction principle; its expression is as follows. Let ( ,𝑑) be a metric space and let : → be a mapping. Then is called a Banach contraction mapping if there exists 𝑘∈[0 ,1 ) such that 𝑑( Q 𝑘𝑑( , )for all , ∈ Then, many mathematicians found

### FIXED POINT RESULTS IN PARTIALLY ORDERED COMPLEX VALUED

ditions satisfying rational inequalities in metric spaces have been developed in a number of works ([17] - [23]). Fixed point theory in partially ordered metric spaces is of relatively recent origin. An early result in this direction is due to Turinici [24] in which xed point problems were studied in partially ordered uniform spaces.

### Fixed Points of Almost Generalized a y) Contractions with

Oct 19, 2016 -contraction mappings and proved fixed point results and its extension to partially ordered metric spaces can be found in [6]. In this direction, we introduce almost generalized (, ) αψ-contractions with rational expression type mappings and establish the existence of fixed points for such mappings in complete partially ordered metric spaces.

### Contractive mappingtheorems inPartially ordered metric spaces

spaces, D-metric spaces, G-metric spaces, F-metric spaces, cone metric spaces, and so on to prove the existing results. Prominent work on the existence and uniqueness of a ﬁxed point and common ﬁxed point theorems involving monotone mappings on cone metric spaces, partially ordered metric

### ISSN : 2454-9150 Coupled Fixed Points For Jungck Type Maps

Then T has a unique fixed point in X. In this paper we mainly prove a unique common coupled fixed point theorem for Jungck type maps satisfying certain rational contraction condition in dislocated quasi b-metric spaces and also we provide an example to illustrate our theorem. We also obtain some recent results as corollaries. II.

### New fixed point results in b-rectangular metric spaces

Abstract. In this work, the class of b-rectangular metric spaces is introduced, some ﬁxed point results dealing with rational type contractions and almost generalized weakly contractive mappings are obtained. Certain examples are given to support the results. Keywords: generalized metric space, rectangular space, b-metric space, Geraghty

### ORDER-THEORETIC FIXED POINT RESULTS FOR ;˚; -GENERALIZED WEAK

Aydi et al. [5] and Imdad et al. [6] almost simultaneously gave some xed point results involving Boyd-Wong-type contractions in partially ordered metric spaces. Nowadays, a vigorous research activity is in progress on this theme and for this kind of activity one can consult [7{14].

### SOME FIXED POINT RESULTS FOR GENERALIZED RATIONAL TYPE

In 2010,Harjani et al. [12] proved a version of Theorem 1.1 in partially ordered metric spaces. In 2011,Luong et al. [22] proved the following theorem for general-ized weak contractions satisfying rational expressions in partially ordered metric spaces, which is a generalization of the result of [12]. [0,∞) such that ψ(t) =0 if and only if t =0.

### Existence of Common Fixed Point for -Metric Rational Type

ﬁxed point of mapping satisfying certain contractive condition in the framework of partially ordered metric spaces. Theorem 1.6. Let (X; ;d) be a partially ordered complete metric space. Let f : X !X be an increasing mapping such that there exists an element x 0 2X with x 0 fx 0. If d(fx;fy) (d(x;y))d(x;y)

### FIXED POINT THEOREMS FOR DUALISTIC CONTRACTIONS OF RATIONAL

FIXED POINT THEOREMS FOR DUALISTIC CONTRACTIONS theorem in the context of partially ordered metric spaces. For more fixed point results, see ([9], [13], [24]). One of the most interesting and important space is partial metric space introduced by Matthews (see [12]) as a part of the study of denotational semantics of

### Available online at http://scik.org Adv. Fixed Point Theory

COUPLED FIXED POINT RESULTS FOR RATIONAL CONTRACTIONS IN METRIC SPACES 103 a contradiction. Thus w =0 and (6) lim n!¥ d(gx n;gx n+1)=0 and lim n!¥ d(gy n;gy n+1)=0: In what follows, we shall prove that fgx ngand fgy ngare Cauchy sequences in X. Suppose the contrary, that at least one of them is not Cauchy. Then there exists an e > 0 for which

### A xed point theorem for Hardy-Rogers type on generalized

in [36]. Abbas in [1] proved some xed point theorems for a T-Hardy-Rogers contraction in the setting of partially ordered partial metric spaces. Some xed point theorems for a generalized almost Hardy-Rogers type F-contraction in metric like space were established by Saipara in [43].