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In the year 2016, Pragadeeswarar et al. [V. Pragadeeswarar, M. Marudai, P. Kumam, J. Nonlinear Sci. Appl., 9 (2016), 1911-1921] considered a special class of multi-valued mappings and investigated the existence of best proximity points for such class of mappings which generalizes the fixed point result established by Choudhury et al. [B. S. Choudhury, N. Metiya, Arab J. Math. Sci., 17 (2011), 135-151] in the context of partially ordered metric spaces. In this note, we have showed that the best proximity point result is a direct consequence of the corresponding fixed point result. In the last part of this note, we applied our result in [V. Pragadeeswarar, M. Marudai, P. Kumam, J. Nonlinear Sci. Appl., 9 (2016), 1911-1921, Example 2.2] to validate our claim. [ABSTRACT FROM AUTHOR]

In this paper, two new inertial CQ-algorithms with strong convergence results are constructed to approximate the solution of the generalized split common fixed point problem: given as a task of finding a point that belongs to the intersection of an infinite family of fixed point sets of demimetric mappings such that its image under an infinite number of linear transformations belongs to the intersection of another infinite family of fixed point sets of demimetric mappings in the image space. The algorithms are established based on the CQ-projection method with inertial effect and step-size selection technique so that the implementation of the proposed algorithms does not need any prior information about the operator norms. The proposed methods improve, complement, and generalize many of the important results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, a new projection-type method for generalized variational inequalities is introduced in Euclidean spaces. Under the assumption that the dual variational inequality has a solution, we show that the proposed method is well-defined and prove that the sequence generated by the proposed method is convergent to a solution, where the condition is strictly weaker than the pseudomonotonicity of the mapping used by some authors. We provide an example to support our results. Compared with the recent works of Li and He [F.-L. Li, Y.-R. He, J. Comput. Appl. Math., 228 (2009), 212-218], and Fang and He [C.-J. Fang, Y.-R. He, Appl. Math. Comput., 217 (2011), 9543-9551], condition (A3) is removed. Moreover, the results presented in this paper also generalize and improve some known results given in other literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notions of θ-φ contraction and θ-φ Suzuki contraction and establish some new fixed point theorems for these mappings in the setting of complete metric spaces. The results presented in the paper improve and extend the corresponding results due to Banach, Browder [F. E. Browder, Nederl. Akad. Wetensch. Proc. Ser. A Indag. Math., 30 (1968), 27-35], Suzuiki [T. Suzuki, Nonlinear Anal., 71 (2009), 5313-5317], Kannan [R. Kannan, Amer. Math. Monthly, 76 (1969), 405-408], Jleli and Samet [M. Jleli, B. Samet, J. Inequal. Appl., 2014 (2014), 8 pages]. Finally, we give an example to illustrate them. c 2017 All rights reserved. [ABSTRACT FROM AUTHOR]

In this paper, a general system of variational inclusions in Banach Spaces is introduced. An iterative method for finding solutions of a general system of variational inclusions with inverse-strongly accretive mappings and common set of fixed points for a λ-strict pseudocontraction is established. Under certain conditions, by forward-backward splitting method, we prove strong convergence theorems in uniformly convex and 2-uniformly smooth Banach spaces. The results presented in the paper improve and extend various results in the existing literatures. Moreover, some applications to monotone variational inequality problem and convex minimization problem are presented. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to prove the multivariate contraction mapping principle of N-variables mappings in Menger probabilistic metric spaces. In order to get the multivariate contraction mapping principle, the product spaces of Menger probabilistic metric spaces are subtly defined which is used as an important method for the expected results. Meanwhile, the relative iterative algorithm of the multivariate fixed point is established. The results of this paper improve and extend the contraction mapping principle of single variable mappings in the probabilistic metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we consider a new parallel algorithm combining viscosity approximation methods to approximate the multiple-set split common fixed point problem governed by demicontractive mappings, and get the generated sequence converges strongly to a solution of this problem. The results obtained in this paper generalize and improve the recent ones announced by many others. [ABSTRACT FROM AUTHOR]

In this paper, we prove some common fixed point theorems for three self-mappings satisfying various new contractive conditions in complete G-metric spaces. We also discuss that these mappings are G-continuous on such a common fixed point. And a non-trivial example is provided to support our new result in the framework of nonsymmetric G-metric spaces. At the end of the results, we give an existence theorem for common solution of three integral equations. The results obtained in this paper differ from the recent relative results in literature. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present the concept of multivariate contraction mapping in a locally convex topological vector spaces and to prove the multivariate contraction mapping principle in such spaces. The neighborhood-type error estimate formulas are also established. The results of this paper improve and extend Banach contraction mapping principle in the new idea. [ABSTRACT FROM AUTHOR]

In this paper, the implicit midpoint rule of asymptotically nonexpansive mapping in CAT(0) spaces is introduced. By the viscosity approximation method, we prove that the proposed implicit iteration converges strongly to a fixed point of asymptotically nonexpansive mapping under certain assumptions imposed on the sequence of parameters. The results presented in the paper improve and extend various results in the existing literature. [ABSTRACT FROM AUTHOR]

In this paper, we define and study the C-integral and strong C-integral of functions mapping a compact interval I0 of ʀm into a real Banach space X. We prove that the C-integral and strong C-integral are equivalent if and only if X is finite dimensional. We also study the relations between the property S8C and strong C-integral. [ABSTRACT FROM AUTHOR]

The purpose of this paper is twofold. First, basic concepts such as Gamma function, almost convergence, fractional order difference operator and sequence spaces are given as a survey character. Thus, the current knowledge about those concepts are presented. Second, we construct the almost convergent spaces with fractional order difference operator and compute dual spaces which help us in the characterization of matrix mappings. After we characterize to the matrix transformations, we give some examples. In this paper, the notation Γ(n) will be shown the Gamma function. For n ∉ {0,-1,-2, . . . }, Gamma function is defined by an improper integral Γ(n) = ∫1∞ 0 e-ttn-1dt. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a projected algorithm with Meir-Keeler contraction for finding the fixed points of the pseudocontractive mappings. We prove that the presented algorithm converges strongly to the fixed point of the pseudocontractive mapping in Hilbert spaces. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a new simultaneous iterative algorithm for the split equality fixed-point problem of demicontractive mappings in real Hilbert spaces and obtain a strong convergence result with no compactness assumptions on the spaces or the mappings and with no extra conditions on the fixed point sets. The results obtained in this paper generalize and improve the recent ones announced by many others. [ABSTRACT FROM AUTHOR]

In this paper, a new iterative algorithm for finding a common element of the set of minimizers of a convex function, the set of solutions of variational inequality problem, the set of solutions of equilibrium problems and the set of fixed points of demicontractive mappings is constructed. Convergence theorems are also proved in Hilbert spaces without any compactness assumption. Furthermore, a numerical example is given to demonstrate the implementability of our algorithm. Our theorems are significant improvements in several important recent results. [ABSTRACT FROM AUTHOR]

In this paper, a new modified proximal point algorithm involving fixed point of nonspreading-type multivalued mappings in Hilbert spaces is proposed. Under suitable conditions, some weak convergence and strong convergence to a common element of the set of minimizers of a convex function and the set of fixed points of the nonspreading-type multivalued mappings in Hilbert space are proved. The presented results in the paper are new. [ABSTRACT FROM AUTHOR]

The aim of this paper is to prove common fixed point theorems for compatible mappings of type (A) for three self-mappings satisfying certain contractive conditions and its topological properties in partial metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, the demiclosed principle of monotone α-nonexpansive mapping is showed in a uniformly convex Banach space with the partial order "⩽". With the help of such a demiclosed principle, the strong convergence of Mann iteration of monotone α-nonexpansive mapping T are proved without some compact conditions such as semi-compactness of T, and the weakly convergent conclusions of such an iteration are studied without the conditions such as Opial's condition. These convergent theorems are obtained under the iterative coefficient satisfying the condition, . . . which contains . . . as a special case. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of a cyclic (α, β)-admissible mapping type S and the notion of an (α, β)-(ψ,φ)-contraction type S. We also establish fixed point results for such contractions along with the cyclic (α, β)-admissibility type S in complete b-metric spaces and provide some examples for supporting our result. Applying our new results, we obtain fixed point results for cyclic mappings and multidimensional fixed point results. As application, the existence of a solution of the nonlinear integral equation is discussed. [ABSTRACT FROM AUTHOR]

In this paper, we prove some fixed point results for a class of α-nonexpansive single and multi-valued mappings in the setting of partial metric spaces. Our results generalize the analogous ones of Vetro [F. Vetro, Filomat, 29 (2015), 2011-2020]. Some examples are presented making our results effective. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new concept of cyclic (α, β)-type γ-FG-contractive mapping and we prove some fixed point theorems for such mappings in complete b-metric spaces. Suitable examples are introduced to verify the main results. As an application, we obtain sufficient conditions for the existence of solutions for nonlinear integral equation which are illustrated by an example. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concepts of multivalued cyclic α-F contraction and triangular α-orbital admissible mappings. We use these concepts to find global best approximation solutions in a metric space with proximally complete property. We also provide some nontrivial examples to support our results. As an application, we obtain best proximity point results in partially ordered metric spaces and best proximity point theorems for single-valued mappings. We also prove fixed point results for multivalued and single-valued α-type F-contractions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the new concept of a generalization of contraction so-called φE-Geraghty contraction and we establish a fixed point theorem for such mappings in complete metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an iterative process which converges strongly to a common fixed point of two mono-pseudocontractive mappings in Banach spaces. Our theorems complement the results that have been proved for the class of pseudocontractive mappings in Banach spaces. [ABSTRACT FROM AUTHOR]

A new modified iterative scheme {xn} is given for the viscosity approximating a common zero of a finite family of accretive mappings fAig in reflexive Banach spaces with a weakly continuous duality mapping J in the present paper. Under certain conditions, we prove the strong convergence of the sequence {xn}. The results here extend and improve the corresponding recent results of some other authors. [ABSTRACT FROM AUTHOR]

We introduce two types of generalized θ-contraction mappings in complete metric spaces. For each type, we study the existence of fixed points. The obtained results in this paper generalize several existing fixed point theorems in the literature. We end this work with some open questions. [ABSTRACT FROM AUTHOR]

In this manuscript, we construct three viscosity implicit iteration schemes based on generalized contractions for strictly pseudo-contractive mappings. The first scheme is used to approximate a fixed point of a single strictly pseudo-contractive mapping, the second scheme is used to approximate a common fixed point of a finite family of strictly pseudo-contractive mappings, the third scheme is used to approximate a common fixed point of a countable family of strictly pseudo-contractive mappings. Furthermore, three strong convergence theorems based on the purposed iterative schemes are established in the framework of Banach spaces. Finally, three numerical examples are also given to show the efficiency and implementation of our schemes. The main results of this paper modify and improve many important recent results in the literature. [ABSTRACT FROM AUTHOR]

The work presented in this paper extends the idea of α-β-contractive mappings in the framework of b-metric spaces. Fixed points are investigated for such kind of mappings. An example is given to show the superiority of our results. As applications we discuss Ulam-Hyres stability, well-posedness and limit shadowing of fixed point problem. [ABSTRACT FROM AUTHOR]

In this paper, we derive a new integral identity concerning differentiable mappings defined on relative convex set. By using the obtained identity as an auxiliary result, we prove some new Simpson-like type inequalities for mappings whose absolute values of the first derivatives are relative semi-(α, m)-logarithmically convex. Several special cases are also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we provide Mazur-Ulam type results for (not necessarily surjective) maps preserving equality of fuzzy distance defined between two fuzzy normed spaces. Our main goal is to study the additivity of such generalizations of fuzzy isometries. As in the classical case, the fuzzy strict convexity of the target space will play an important role. [ABSTRACT FROM AUTHOR]

In this paper, by using the measure of noncompactness and Meir-Keeler type mappings, we prove some new fixed point theorems for some certain mappings, namely, the weaker ϕ-Meir-Keeler type contractions, asymptotic weaker ϕ-Meir-Keeler type contractions, asymptotic sequence {øi}-Meir-Keeler type contraction, ξ-generalized comparison type contraction, and R-functional type ψ-contractions. Our results improve and hence cover the well-known Darbo's fixed point theorem, and several related recent fixed point results. [ABSTRACT FROM AUTHOR]

Four fixed point theorems for mappings satisfying contractive conditions of integral type in complete metric spaces are proved. The results presented in this paper extend and improve a few results existing in literature. Two examples involving the contractive mappings of integral type are constructed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of α-dominated multivalued mappings and establish the existence of common fixed points of such mappings on a closed ball contained in left/right K-sequentially complete dislocated quasi b-metric spaces. These results improve, generalize, extend, unify, and complement various comparable results in the existing literature. Our results not only extend some primary results to left/right K-sequentially dislocated quasi b-metric spaces but also restrict the contractive conditions on a closed ball only. Some examples are presented to support the results proved herein. Finally as an application, we obtain some common fixed point results for single-valued mappings by an application of the corresponding results for multivalued mappings satisfying the contractive conditions more general than Banach type and Kannan type contractive conditions on closed balls in a left K-sequentially complete dislocated quasi b-metric space endowed with an arbitrary binary relation. [ABSTRACT FROM AUTHOR]

In this paper, we establish some new common tripled fixed point theorems for mappings defined on a set equipped with two rectangular b-metrics. We also provide illustrative examples in support of our new results. In the end of the paper, we give an existence and uniqueness theorem for a class of nonlinear integral equations by using the obtained result. The results presented in this paper generalize the well-known comparable results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we establish some common fixed point theorems for four mappings satisfying C' iric' type contractive condition in b-metric spaces without any completeness assumption. Our results improve and generalize the results in the very recent papers ([Z.-Z. Yang, H. Sadati, S. Sedghi, N. Shobe, J. Nonlinear Sci. Appl., 8 (2015), 1022-1031], [V. Ozturk, S. Radenovi'c, SpringerPlus, 5 (2016), 10 pages]). Particularly, the contractive constant k/b² in the result of Yang et al. is enlarged to k/b. Some examples are provided to support our results. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study the problem of the system of N fixed point operator equations with N-variables pseudo-contractive mapping. Firstly, the concept of N-variables pseudo-contractive mapping and relatively concepts of nonlinear mappings are presented in Banach spaces. Secondly, the existence theorems of solutions for the system of N fixed point operator equations with N-variables pseudo-contractive mapping are proved in reflexive Banach spaces by using the method of product spaces. In order to get the expected results, the normalized duality mapping of product Banach spaces is defined. Meanwhile the reflexivity of the product of reflexive Banach spaces and Opial's condition of product spaces of Banach spaces are also discussed. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of weak Weak θ-φ-contraction ensuring a convergence of successive approximations but does not force the mapping to be continuous at the fixed point. Thus, we answer one more solution to the open question raised by Rhoades in [B. E. Rhoades, Fixed point theory Appl, Berkeley, CA, (1986), Contemp. Math., Amer. Math. Soc., Providence, RI, 72 (1988), 233-245]. [ABSTRACT FROM AUTHOR]

In this paper, first, we introduce several types of the Ulam-Hyers stability, the well-posedness and the limit shadowing property of fixed point problems in Ms-metric spaces. Second, we give such results for fixed point problems of Banach and Kannan contractive mappings in Ms-metric spaces. Finally, we give some examples to illustrate the validity of our main results. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce a new set-valued mapping by the scalar approximate solution mapping of a parametric generalized weak vector equilibrium problem and obtain some of its properties. By one of obtained properties, we establish the lower semicontinuity the approximate solution mapping to a parametric generalized weak vector equilibrium problem without the assumptions about monotonicity and approximate solution mappings. Simultaneously, under some suitable conditions, we obtain the upper semicontinuity of the approximate solution mapping to a generalized parametric weak vector equilibrium problem. Our main results improve and extend the corresponding ones in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we prove some results on the existence of fixed points for multivalued maps with respect to general distance. Our results improve and generalize a number of known fixed point results including the fixed point results [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new concept called partial (h-F)-generalized (and (h-F)-subgeneralized) convex contractions of order 3 (and with rank 3) using some auxiliary functions. Also we present some approximate fixed point results in metric space and approximate fixed point results in metric space endowed with a graph. Some examples are provided to illustrate the main results and to show the essentiality of the given hypotheses. [ABSTRACT FROM AUTHOR]

In this paper, we introduce several types of S-γ-Φ-φ-contractive mappings which are generalizations of α-ψ-contractive mappings [B. Samet, C. Vetro, P. Vetro, Nonlinear Anal., 75 (2012), 2154-2165] in the structure of S-metric spaces. Furthermore, we prove existence and uniqueness of fixed points and common fixed points of such contractive mappings. Our results generalize, extend and improve the existing results in the literature. We also state some illustrative examples to support our results. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence and uniqueness of fixed points for a new class of contractive mappings involving rational expressions, which enable us to extend many known results in the literature. We consider illustrative example and consequences to underline the novelty of the main results. [ABSTRACT FROM AUTHOR]

In this paper, considering an order relation on a vector metric space which is introduced by C, evik and Altun in 2009, we present some fundamental fixed point results. Then, we provide some nontrivial examples show that the investigation of this work is significant. [ABSTRACT FROM AUTHOR]

In this paper, the re-defined generalized metric space which is equivalent to the generalized metric spaces defined by Jleli and Samet is presented so that some well-known spaces are incorporated in the area of re-defined generalized metric spaces. Some fixed point existence and uniqueness results of contractive and generalized contraction mappings defined on such metric spaces are provided. Especially, we discussed the fixed point existence results of Ćirić-Maiti-Pal orbit mappings of contractive type in the re-defined generalized metric spaces. In addition, some examples are provided to better support the fixed point results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce α-ψ-Φ Jachymski contractive mappings with generalized altering distance functions in the setting of quasi-metric spaces. Some theorems on the existence and uniqueness of fixed points for such mappings via admissible mappings are established. Utilizing above abstract results, we derive common fixed point theorem for two operators and multidimensional fixed point results for nonlinear mappings satisfying different kinds of contractive conditions on partially ordered metric spaces. Moreover, we present some examples and applications in a Fredholm integral equation and an initial value problem for partial differential equation of parabolic type. [ABSTRACT FROM AUTHOR]

Let (X, d, K) be a cone b-metric space over a ordered Banach space (E,≿) with respect to cone P. In this paper, we study two problems: (1) We introduce a b-metric ρc and we prove that the b-metric space induced by b-metric ρc has the same topological structures with the cone b-metric space. (2) We prove the existence of the coincidence point of two mappings T, f : X → X satisfying a new quasi-contraction of the type d(Tx, Ty) ≿ Λ{d(fx, fy), d(fx, Ty), d(fx, Tx), d(fy, Ty), d(fy, Tx)g, where Λ : E → E is a linear positive operator and the spectral radius of KΛ is less than 1. Our results are new and extend the recent results of [N. Hussain, M. H. Shah, Comput. Math. Appl., 62 (2011), 1677-1684], [M. Cvetković, V. Rakočević, Appl. Math. Comput., 237 (2014), 712-722], [Z. Kadelburg, S. Radenović, J. Nonlinear Sci. Appl., 3 (2010), 193-202]. [ABSTRACT FROM AUTHOR]

In this paper, fixed point properties for a class of more generalized nonexpansive mappings called (L)-type mappings are studied in geodesic spaces. Existence of fixed point theorem, demiclosed principle, common fixed point theorem of single-valued and set- valued are obtained in the third section.Moreover, in the last section,∆-convergence and strong convergence theorems for (L)-type mappings are proved. Our results extend the fixed point results of Suzuki's results in 2008 and Llorens-Fuster's results in 2011. [ABSTRACT FROM AUTHOR]

In this paper, we give a negative answer to the open question raised by Radenovic et al. [S. Radenović, T. Dośenović, T. A. Lampert, Z. Golubov ĩ ć, Appl. Math. Comput., 273 (2016), 155-164]. Namely, we give two examples which show that the set of fixed points for cyclic quasi-contractive mappings of Ćirićtype may be empty. Then, by using a new lemma, we give some sufficient conditions for the existence of fixed point for cyclic and non-cyclic quasi-contractive mappings of ĆiriĆtype in b-metric spaces. In particular, we show that the condition of Fatou property in the result of Amini-Harandi [A. Amini-Harandi, Fixed Point Theory, 15 (2014), 351-358] may be omitted. [ABSTRACT FROM AUTHOR]

In this paper, we first introduce the notions of (α β)-generalized hybrid set-valued mappings, strongly attractive points,attractive points and condition Í. Then we construct an iterative method for finding attractive points of (α β)-generalized hybrid set-valued mappings and obtain some convergence theorems of the proposed iterative scheme for (α β)-generalized hybrid set-valued mappings defined on a uniformly convex Banach space by using of condition I' and demicompact property,respectively. [ABSTRACT FROM AUTHOR]