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In this paper, some fixed point theorems in a partial b-metric space endowed with a partial order are proved. The results of this paper generalize and extend the Banach contraction principle and some other known results in partial b-metric spaces endowed with a partial order. Some examples are given which illustrate the cases when new results can be applied while old ones cannot. [ABSTRACT FROM AUTHOR]

In this paper, we prove some coupled coincidence point results for mixed g-monotone mappings in partially ordered metric spaces via new functions. The main results of this paper are generalizations of the main results of Luong and Thuan [ N.V. Luong, N.X. Thuan, Coupled fixed points in partially ordered metric spaces and application, Nonlinear Anal. 74 (2011) 983- 992]. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the existence of some common best proximity point theorems for generalized Lipschitz contractive mappings on cone b-metric spaces over Banach algebras without assumption of normality. Our results generalize the corresponding result by Xu and Radenović (Fixed Point Theory and Appl. 2014, 2014: 102) and by Huang and Radenović (J. Computational Anal. and Appl. 2016, 20(3)). Further, we give an example to illustrate that our works are never equivalent with the counterparts in the literature. [ABSTRACT FROM AUTHOR]

Saadati et al [1] introduced the notion of Ω-distance mappings and studied some existing fixed point results. In this paper, we employ the notion of Ω-distance and some functions defined on [0,∞) to introduce some new nonlinear contractions of Suzuki types. We utilize our new notions toformulate and proved serval fixed and common fixed point results. Our results improve and extend many results in literature. [ABSTRACT FROM AUTHOR]

This paper is a continuation of the investigations of F-contractions. The aim of this article is to extend the concept of Ciric type F-contraction on a closed ball. We presented the notion of F-contraction on a closed ball and introduced a new approach of fixed point theorems for Fcontraction on a closed ball in a complete metric space. Our results are very useful for the contraction of the mapping only on closed ball instead of the whole space. Some comparative examples are constructed which illustrate the superiority of our results. Our results provide extension as well as substantial generalizations and improvements of several well-known results in the existing comparable literature. [ABSTRACT FROM AUTHOR]

Let (x,d) be a Polish space, CB(X) the family all nonempty closed and bounded subsets of X and (Ω, X) be a measurable space. In this paper, a pair of hybrid measurable mappings f: Ω ×; X → X and T:Ω ×; X → CB(X), satisfying non-expansive type condition; H(T(ω, y), ⩽(ω, d)) ⩽ ɑ(ω)d(f(ω, x), f(ω, y)) + b(ω) max{d(f(ω, x), d(f, ω)), d(f(ω, y), T(ω, y))} +c(ω)[d(f(ω, x), T(ω, y)) + d(f(ω, y), T(ω, x))] for every x, y ∊ X, where a, b, c: Ω → [0,1) are measurable mappings such that for all ω ∊ Ω, b(ω) > 0, c(ω) > 0 and a(ω) + b(ω) + 2c(ω) = 1, are introduced and investigated. It is proved that if X is complete, T(ω, . ), f(ω, . ) are continuous for all ω ∊ Ω, T(., x), f(., x) are measurable for all x ∊ X and T(ω, ξ(ω)) ⊆ f(ω × X) and f(ω × X) = X for each ω ∊ Ω,, then there is a measurable mapping ξ: Ω → X such that f(ω, ξ(ω)) ⊆ T(, ξ(ω)) for all ω ω∊ Ω .This result generalizes and extends the fixed point theorems of Papageorgiou [21], Ciric et al.[8], Jhade et al. [16] and many classical fixed point theorems. We also discuss an illustrative example to highlight the realized improvements. [ABSTRACT FROM AUTHOR]

In this paper, we present a unique common fixed point theorem for pointwise R-weakly commuting maps in complete multiplicative metric space. Another result of R-weakly commuting of type (P) is also established. Our results generalize the results of the main theorem of Xiaoju He, Meimei Song and Danping Chen (Common fixed points for weak commutative mappings ona multiplicative metric space) by using R-weakly commuting maps. [ABSTRACT FROM AUTHOR]

In this paper, we have established some coupled fixed point theorems for α -Geraghty type contractive mappings in the context of partially ordered metric spaces. Applying these results, we have deduced fixed point results on metric spaces endowed with the graph. Also, the effectiveness of our work is validated with the help of a suitable example. [ABSTRACT FROM AUTHOR]

In this paper, we have presented some common fixed point results for the contractive mappings on complex valued bmetric spaces and obtained a generalization of the theorem of Azam et al., [2], Klin-eam and Suanoom [7], Mukheimer [8], Rouzkard and Imdad [12], Sitthikul and Saejung [13] and Sintunavarat and Kumam[14]. Further, our result is supported by examples. [ABSTRACT FROM AUTHOR]

In this paper, we establish some common fixed point theorems for two mappings satisfying set-valued Prešić- Chatterjea type contractive conditions. The new theorems generalize and unify some well-known theorems of the literature. We also provide some examples to illustrate and confirm the usability of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce W* -spaces which generalizes W -spaces introduced by Piao and Jin [10] and prove three unique common fixed point theorems in it. Some illustrative examples to highlight the results are furnished. [ABSTRACT FROM AUTHOR]

The intent of this paper is to introduce the concept of Gb-cone metric and we describe some basic properties of such metric. Further, we establish some fixed point theorems for self-mappings satisfying the contractive type conditions and a common fixed theorem for two weakly compatible self-mappings satisfying the contractive condition in Gbcone metric spaces without the assumption of normality. Moreover, some examples are provided to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper, we first define the new notion of fuzzy uniform normal structure. Moreover, we prove that the spectrum of the category of fuzzy reflexive spaces is broader than the category of the spaces which have fuzzy normal structure. Also, we introduce the notions of FNST, FNSTN and we prove the theorems of the fixed points of some classes of mappings on the sets from the fuzzy reflexive space, which have some of the properties FNST, FNSTN. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a common fixed point theorem by employing the notion of g -reciprocal continuity in probabilistic metric space. We demonstrate that g -reciprocal continuity ensures the existence of common fixed point under strict contractive conditions, which otherwise do not ensure the existence of fixed points. [ABSTRACT FROM AUTHOR]

In this paper, we prove some common fixed point theorems for a pair of weakly compatible mappings satisfying (Ψ, α, β)-weak contractions in fuzzy metric spaces employing a control function. Our results improve and generalize several previously known relevant results of the existing literature. Some illustrative examples are alsofurnished to substantiate our main results. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some common fixed point theorems for recently introduced notion of on a set X equipped with the function F: X × X → Δ without using the triangle inequality besides relaxing symmetric condition. Our results extend the results of Pathak and Rai. [Common fixed points for PD-operator pairs under relaxed conditions with applications, Journal of Computational and Applied Mathematics 239(1)(2013) 103-113], Hussain et al.[Common fixed points for JH-operators and occasionally weakly biased pairs under relaxed conditions, Nonlinear Anal.74(2011) 2133-2140], Bhatt et al.[Common fixed point theorems for occasionally weakly compatible mappings under relaxed conditions, Non-linear analysis Theory, Methods and appl. 73(2010) 176-182] and several others. [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove fixed point theorem with PPF dependence for mappings involving (ø,ψ) - rational type contraction in Razumikhin class. Our result extends and generalizes the result of Jaggi [9]. [ABSTRACT FROM AUTHOR]

In 2006, Mustafa and Sims [18-19] introduced an improved version of the generalized metric space structure which they called G-metric spaces and in 2011; Berinde and Borcut [11] introduced the concept of triple fixed point. The intent of this paper is to establish some tripled fixed point theorems for mappings having mixed monotone property under nonlinear type contractions depended on another function in the framework of a G-metric space X enclosed with partial order. The presented results generalize, improve and extend corresponding results of H. Aydi et al. [13] (Tripled Fixed Point Results in Generalized Metric Spaces" Journal of Applied Mathematics Volume 2012, Article ID 314279, 10 pages, doi:10.1155/2012/314279). Moreover, some examples are provided to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

Matthews [10] introduced a new distance P on a nonempty set X, which he called a partial metric. Sonmez [16] introduced the notion of partial cone metric space and its topological characterization. In present paper, we define expansive map in partial cone metric space and prove some fixed point theorems for such maps. Our results extend the results of [4, 9, and 17] in partial cone metric space. An example is given to support the usability of our results. [ABSTRACT FROM AUTHOR]

Matthews [10] introduced a new distance P on a nonempty set X, which he called a partial metric. Sonmez [16] introduced the notion of partial cone metric space and its topological characterization. In present paper, we define expansive map in partial cone metric space and prove some fixed point theorems for such maps. Our results extend the results of [4, 9, and 17] in partial cone metric space. An example is given to support the usability of our results. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish common fixed point theorems for single valued maps satisfying general contractive conditions of integral type using weak compatibility wherein the conditions of completeness of the underlying subspaces and containment of ranges amongst involved maps is not needed. Moreover, an example and an application are also given to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

In this paper a general fixed point theorem for two pairs of weakly compatible mappings satisfying Φ - implicit relations in G - metric spaces, which generalize and improve Theorem 2.1 [9], is proved. [ABSTRACT FROM AUTHOR]