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In this paper, we present some fixed point results for generalized θ‐ϕ‐contraction in the framework of α,η−compete rectangular b‐metric spaces. Further, we establish some fixed point theorems for this type of mappings defined on such spaces. Our results generalize and improve many of the well-known results. Moreover, to support our main results, we give an illustrative example.

The aim of this work is to obtain fixed point results for multivalued mappings satisfying generalized contractions on the intersection of an open ball and a sequence in left (right) K-sequentially complete ordered dislocated quasi metric space. An example has been built to demonstrate the novelty of results. Our results generalize and extend the results of Altun et al. (J. Funct. Spaces, Article ID 6759320, 2016)

In this paper, we establish a fixed point theorem for generalized contraction mappings in b-metric spaces endowed with a digraph. As an application of this result, we obtain fixed points of cyclical mappings in the setting of b-metric spaces. Our results extend and generalize several existing results in the literature.

The purpose of this paper is to study the coupled fixed point problem and the coupled best proximity problem for single-valued and multi-valued contraction type operators defined on cyclic representations of the space. The approach is based on fixed point results for appropriate operators generated by the initial problems.

In this paper, we prove some fixed points, coupled coincidence point and coupled common fixed point results for mappings satisfying an almost generalized contraction conditions in partially ordered [Formula: see text]-metric spaces. These results generalize, extend and unify many comparable results in the existing literature. Few examples are given to support our results.

The purpose of this paper is to prove that instead of a rational contraction shown in the papers Afrah A. N. Abdou, \emph{Fixed point theorems for generalized contraction mappings in multiplicative metric spaces, }J. Nonlinear Sci.Appl. 9, 2347-2363, (2016) and N. Sharma, K. Kumar, S. Sharma, R. Jha, \emph{Rational contractive conditionin multiplicative metric space and common fixed point theorem}, International Journal of Innovative Research in Science,Engineering and Technology, 5, 10473-10480 (2016) a more general contractive condition can be obtained in multiplicative metric spaces, which is equivalent to a contractive condition in metric spaces.

In this paper, we prove some theorems and a common fixed point theorem in vector metric spaces for generalized contraction mappings and give an example.

We introduce the notion of generalized θ-ϕ contraction and establish some new fixed point theorems for this contraction in the setting of complete G-metric spaces. The results presented in the paper improve, extend, and unify some known results. Finally, we give an example to illustrate them.

In the present article, we study some fixed point theorems for a hybrid class of generalized contractive operators in the context of b-rectangular metric spaces. An open problem regarding to further generalizations for this type of operators is also given.

This papaer has been published in Far East Journal of Mathematical Sciences (FJMS) Vol. 101, No. 8, 2017, pp 1813-1832

We have introduced the new notions of R-weakly graph preserving and R-weakly &alpha, admissible pair of multivalued mappings which includes the class of graph preserving mappings, weak graph preserving mappings as well as &alpha, admissible mappings of type S, &alpha, * -admissible mappings of type S and &alpha, * - orbital admissible mappings of type S respectively. Some generalized contraction and rational contraction classes are also introduced for a pair of multivalued mappings and common fixed point theorems are proved in a b-metric space endowed with a graph. We have also applied our results to obtain common fixed point theorems for R-weakly &alpha, admissible pair of multivalued mappings in a b-metric space which are the proper extension and generalization of many known results. Proper examples are provided in support of our results. Our main results and its consequences improve, generalize and extend many known fixed point results existing in literature.

In this paper we define the tangential property in partial metric spaces to prove a common fixed point theorems for two pairs of self mappings, which satisfying a generalized weak contractive condition as well as satisfying a generalized contraction, an example is given to illustrate ours results.

In this paper, we propose and prove the common fixed point theorems on generalized contraction mappings in extended rectangular b-metric spaces by utilizing the weakly compatible function property.

In this article, we establish fixed point results for a pair of multivalued mappings satisfying generalized contraction on a sequence in dislocated b-quasi metric spaces and Fρs⁎ Khan type contraction on a sequence in b-quasi metric spaces. An example and an application have been discussed. Our results modify and generalize many existing results in literature.

In this paper, we introduce weakly generalized contraction conditions on G-metric space and prove some common fixed point theorems for the proposed contractions. The results in this paper differ from the recent corresponding results given by some authors in literature.

In this paper, we present some coincidence and common fixed point results for infinite families of contractive maps satisfying a new class of pairs of generalized contractive type mappings defined in partial metric spaces. Our results extend and generalize many known results in the literature. Also, we introduce an example to support the validity of our results.

In this paper, we introduce the concept of generalized contraction for multivalued operators defined on ordered complete metric spaces. We analyze the existence of fixed points for generalized multivalued operators. Moreover, as an application of our main theorem, we give an existence theorem for the solution of a hyperbolic differential inclusion problem.

In this paper, we introduced and studied a new class of mappings in ordered metric spaces that is inspired from the concept of a P-function introduced in Chaipunya et. al. [10]. With our new class, we furnish fixed point theorems for continuous, noncontinuous, monotonic, and nonmonotonic mappings in various kinds of the ordering structures.

The purpose of this paper is to study common fixed points in complex valued metric spaces and obtain sufficient conditions for the existence of common fixed points of a pair of mappings satisfying generalized contraction involving rational expressions.

The purpose of this paper is to prove the n fixed point theorems and n best proximity point theorems for generalized contraction in partially ordered metric spaces. We firstly investigate the n fixed point theorems. And on this basis, we obtain the n best proximity point theorems using P-operator technique. Many recent results in this area have been generalized and improved.

By using the idea of Pata [V. Pata, A fixed point theorem in metric spaces. J. Fixed Point Theory Appl. 10 (2011) 299–305.] we establish a new common fixed point theorem and as an application, we prove the existence and uniqueness of common solutions for a class of system of functional equations arising in dynamic programming.

Mathematical models have extensively been used in problems related to engineering, computer sciences, economics, social, natural and medical sciences etc. It has become very common to use mathematical tools to solve, study the behavior and different aspects of a system and its different subsystems. Because of various uncertainties arising in real world situations, methods of classical mathematics may not be successfully applied to solve them. Thus, new mathematical theories such as probability theory and fuzzy set theory have been introduced by mathematicians and computer scientists to handle the problems associated with the uncertainties of a model. But there are certain deficiencies pertaining to the parametrization in fuzzy set theory. Soft set theory aims to provide enough tools in the form of parameters to deal with the uncertainty in a data and to represent it in a useful way. The distinguishing attribute of soft set theory is that unlike probability theory and fuzzy set theory, it does not uphold a precise quantity. This attribute has facilitated applications in decision making, demand analysis, forecasting, information sciences, mathematics and other disciplines. In this thesis we will discuss several algebraic and topological properties of soft sets and fuzzy soft sets. Since soft sets can be considered as setvalued maps, the study of fixed point theory for multivalued maps on soft topological spaces and on other related structures will be also explored. The contributions of the study carried out in this thesis can be summarized as follows: i) Revisit of basic operations in soft set theory and proving some new results based on these modifications which would certainly set a new dimension to explore this theory further and would help to extend its limits further in different directions. Our findings can be applied to develop and modify the existing literature on soft topological spaces ii) Defining some new classes of mappings and then proving the existence and uniqueness of such mappings which can be viewed as a positive contribution towards an advancement of metric fixed point theory iii) Initiative of soft fixed point theory in framework of soft metric spaces and proving the results lying at the intersection of soft set theory and fixed point theory which would help in establishing a bridge between these two flourishing areas of research. iv) This study is also a starting point for the future research in the area of fuzzy soft fixed point theory., Abbas, M. (2014). Soft Set Theory: Generalizations, Fixed Point Theorems, and Applications [Tesis doctoral no publicada]. Universitat Politècnica de València. doi:10.4995/Thesis/10251/48470., TESIS

The present paper deals with few fixed point results for mappings satisfying some generalized contractive type inequality condition in 2-metric spaces, wh ich generalize the results of Rhoades (1979) and Gahler (1963), Iseki (1975), Iseki et.al (1976) in turn. The inqualities involve a rational type of terms given by ( ρ x ,f x ,a + ρ(y,f x ,a) 2 ) , ( ρ x ,f y ,a + ρ(y,f x ,a) 2 ) , ( ρ x ,g y ,a + ρ(y ,f x ,a) 2 ), (ρ(x,fj mj (y),a) + ρ(y,fi mi (x),a)) / 2 etc under max co mposition.

In this work, we study some new common fixed point results for generalized contractive multi-valued non-self-mappings on complete metric spaces.

In this paper, we prove fixed point theorems for generally contractive mappings in complete partial metric spaces. Theorems presented are generalizations of recent fixed point theorems of D. Ilic, V. Pavlovic, and V. Rakocevic. An example is also stated that illustrates our results are extensions of their theorems.

Using the concept of u-distance, a fixed point problem in metric spaces for closed valued maps, is solved. Consequently, several known fixed point results are either improved or generalized.

The main aim of this paper, we prove some common fixed point results in the framework of metric and partially ordered metric spaces satisfying a generalized contractive condition of rational type. The proved results generalize and extend some known results in the literature.

We introduce the generalized almost ( &phi, &theta, ) -contractions by means of comparison type functions and another kind of mappings endowed with specific properties in the setting of dualistic partial metric spaces. Also, generalized almost &theta, Geraghty contractions in the setting of dualistic partial metric spaces are defined by the use of a function of Geraghty type and another adequate auxiliary function. For these classes of generalized contractions, we have stated and proved the existence and uniqueness of a best proximity point.

The aim of this paper is to extend a very recent result proved by Doric (2009) [4] , as well as other theorems given by Rhoades (2001) [2] and Dutta and Choudhury (2008) [3] .

In this paper we introduce the class of generalized ( ψ , φ ) -weak contractive mappings. We establish that these mappings necessarily have a unique common fixed point in complete metric spaces. This result generalizes an existing result in metric spaces.

[EN] In this paper we introduce the notion of modified w-distance (mw-distance) on a quasi-metric space which generalizes the concept of quasi-metric. We obtain a fixed point theorem for generalized contractions with respect to mw-distances on complete quasi-metric spaces., The authors acknowledge the support of the Ministry of Economy and Competitiveness of Spain, Grant MTM2012-37894-C02-01.

The aim of this paper is to prove a more generalized contraction mapping principle. By using this more generalized contraction mapping principle, a further generalized best proximity theorem was established. Some concrete results have been derived by using the above two theorems. The results of this paper improve many important results published recently in the literature.

In this paper, we introduce the notion of Generalized contractive type mappings in complex valued metric space and establish fixed point theorem for these mappings.

We correct the proof of Theorem 1 in the paper in the title.

We obtain a fixed point theorem for generalized contractions on complete quasi-metric spaces, which involves w-distances and functions of Meir-Keeler and Jachymski type. Our result generalizes in various directions the celebrated fixed point theorems of Boyd and Wong, and Matkowski. Some illustrative examples are also given., The authors are grateful to the referees for several useful suggestions. They also thank the support of the Ministry of Economy and Competitiveness of Spain, Grant MTM2012-37894-C02-01.