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In this paper, we introduce generalizations of the concept of MR-Kannan type contractions and utilize those conditions to derive new fixed point theorems under both contractive and non-contractive conditions. Our approach enhances various existing results related to enriched mappings. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new iteration process which is faster than the leading; S [J. Nonlinear Convex Anal. 8, no. 1 (2007), 61{79], Thakur et al. [App. Math. Comp. 275 (2016), 147{155] and M [Filomat 32, no. 1 (2018), 187{196] iterations for numerical reckoning fixed points. Using this new iteration process, some fixed point convergence results for generalized ff-nonexpansive mappings in the setting of uniformly convex Banach spaces are proved. At the end of paper, we offer a numerical example to compare the rate of convergence of the proposed iteration process with the leading iteration processes. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two new classes of nonlinear mappings and present some new existence and convergence theorems for these mappings in Banach spaces. More precisely, we employ the Krasnosel'ski iterative method to obtain fixed points of Suzuki-enriched nonexpansive mappings under different conditions. Moreover, we ap-proximate the fixed point of enriched-quasinonexpansive mappings via Ishikawa iterative method. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to introduce the class of enriched interpolative Kannan type operators on Banach space that contains the classes of enriched Kannan operators, interpolative Kannan type contraction operators and some other classes of nonlinear operators. Some examples are presented to support the concepts introduced herein. A convergence theorem for the Krasnoselskii iteration method to approximate fixed point of the enriched interpolative Kannan type operators is proved. We study well-posedness, Ulam-Hyers stability and periodic point property of operators introduced herein. As an application of the main result, variational inequality problem is solved. [ABSTRACT FROM AUTHOR]

The main purpose of this paper is to introduce a viscosity-type proximal point algorithm, comprising of a nonexpansive mapping and a finite sum of resolvent operators associated with monotone bifunctions. A strong convergence of the proposed algorithm to a common solution of a finite family of equilibrium problems and fixed point problem for a nonexpansive mapping is established in a Hadamard space. We further applied our results to solve some optimization problems in Hadamard spaces. [ABSTRACT FROM AUTHOR]

Kirk introduced the notion of pointwise eventually asymptotically non-expansive mappings and proved that uniformly convex Banach spaces have the fixed point property for pointwise eventually asymptotically nonexpansive maps. Further, Kirk raised the following question: "Does a Banach space X have the fixed point property for pointwise eventually asymptotically nonexpansive mappings whenever X has the fixed point property for nonexpansive mappings?". In this paper, we prove that a Banach space X has the fixed point property for pointwise eventually asymptotically nonexpansive maps if X has uniform normal sturcture or X is uniformly convex in every direction with the Maluta constant D(X) < 1. Also, we study the asymptotic behavior of the sequence {Tnx} for a pointwise eventually asymptotically nonexpansive map T defined on a nonempty weakly compact convex subset K of a Banach space X whenever X satisfies the uniform Opial condition or X has a weakly continuous duality map. [ABSTRACT FROM AUTHOR]

We consider a new class of nonlinear mappings that generalizes two well-known classes of nonexpansive type mappings and extends some other classes of mappings. We present some existence and convergence results for this class of mappings. Some illustrative examples presented herein show the generality of the obtained results. [ABSTRACT FROM AUTHOR]

A Meir-Keeler type fixed point theorem for a family of mappings is proved in Menger probabilistic metric space (Menger PM-space). We establish that completeness of the space is equivalent to fixed point property for a larger class of mappings that includes continuous as well as discontinuous mappings. In addition to it, a probabilistic fixed point theorem satisfying (o-d) type non-expansive mappings is established. [ABSTRACT FROM AUTHOR]

In this article, we introduce the concept of a soft quasi-pseudometric space. We show that every soft quasi-pseudometric induces a compatible quasi-pseudometric on the collection of all soft points of the absolute soft set whenever the parameter set is finite. We then introduce the concept of soft Isbell convexity and show that a self non-expansive map of a soft quasi-metric space has a nonempty soft Isbell convex fixed point set. [ABSTRACT FROM AUTHOR]

We consider a wider class of nonexpansive type mappings and present some fixed point results for this class of mappings in hyperbolic spaces. Indeed, first we obtain some existence results for this class of mappings. Next, we present some convergence results for an iteration algorithm for the same class of mappings. Some illustrative non-trivial examples have also been discussed. [ABSTRACT FROM AUTHOR]

In this manuscript we introduce a new class of monotone generalized nonexpansive mappings and establish some weak and strong convergence theorems for Krasnoselskii iteration in the setting of a Banach space with partial order. We consider also an application to the space L1([0,1]). Our results generalize and unify the several related results in the literature. [ABSTRACT FROM AUTHOR]

In this article, we prove a fixed point theorem for cyclic relatively non-expansive mappings in the setting of generalized semimetric spaces by using a geometric notion of seminormal structure and then we conclude a result in uniformly convex Banach spaces. We also discuss on the stability of seminormal structure in generalized semimetric spaces. [ABSTRACT FROM AUTHOR]