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In this paper, we introduce the notion of $$\alpha $$ -integral type G-contraction mappings to generalize the notions of Banach G-contraction and integral G-contraction mappings. We also prove some fixed point theorems for $$\alpha $$ -integral type G-contraction mappings. By providing some example, we show that our results are real generalization of several results in literature. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new iterative algorithm to approximate fixed points of total asymptotically nonexpansive mappings in $\operatorname{CAT}(0)$ spaces. We also provide two examples to illustrate the convergence behavior of the proposed algorithm and numerically compare the convergence of the proposed iteration scheme with the existing schemes. [ABSTRACT FROM AUTHOR]

In this paper, the notion of α-ψ-contractive mappings in the setting of w-distance is introduced and some new fixed point theorems for such mappings are established. Presented fixed point theorems generalize recent results of Samet et al. [Nonlinear Anal. 75 (2012), 2154-2165] and others. Moreover, some examples and an application to nonlinear fractional differential equations are given to illustrate the usability of the new theory. [ABSTRACT FROM AUTHOR]

In this paper, we aim to introduce new types of α-admissibility in the framework of b-metric spaces. Some examples to show the independently of each type of α-admissibility are given. Using these concepts, fixed point theorems satisfying generalized weak contractive condition in the setting of b-metric spaces are established. We furnish an illustrative example to demonstrate the validity of the hypotheses and the degree of utility of our results. As an application, we discuss the existence of a solution for the following nonlinear integral equation: where $${a, b \in {\mathbb{R}}}$$ such that $${a < b, x \in C[a, b]}$$ (the set of all continuous functions from [ a, b] into $${{\mathbb{R}}}$$ ), $${\phi : [a, b] \rightarrow {\mathbb{R}}}$$ and $${K : [a, b] \times [a, b] \times {\mathbb{R}} \rightarrow {\mathbb{R}}}$$ are given mappings. [ABSTRACT FROM AUTHOR]

The aim of this work is to introduce some new notions of generalized convex contraction mappings and establish some approximate fixed point theorems for such mappings in the setting of complete metric spaces. Examples and application to approximate fixed point results for cyclic mappings are also given in order to illustrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

In this work we present a new type of stability results for generalized Cauchy functional equation of the form where $${a, b \in \mathbb{N}}$$ and $${f}$$ is a mapping from a commutative semigroup ( $${G_1, \ast}$$ ) to a commutative group ( $${G_2, \diamond}$$ ). Using this form we generalize, extend and complement some earlier classical results concerning the stability of additive Cauchy functional equations. Our results are improvement and generalization of main results of Brzdȩk [Fixed Point Theory Appl. 2013 (), doi::285] and many results in literature. Some of the stability results for many types of functional equations are given here to illustrate the usability of the obtained results. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to obtain some new common fixed point theorems for weakly compatible mappings in fuzzy metric spaces (in the sense of Kramosil and Michálek) satisfying new contractive conditions employing the common limit in the range property. Our results generalize and extend some recent results contained in Jain et al. (2012) [12] to generalized contractive conditions under some control functions. In the process, some results about multidimensional common fixed points as coupled/tripled/quadrupled common fixed point results are derived from our main results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of partial α-ψ contractive mappings along with generalized metric distance. We also establish the existence of fixed point theorems for such mappings in generalized metric spaces. Our results extend and unify main results of Karapinar [E. Karapinar, Abstr. Appl. Anal., 2014 (2014), 7 pages] and several well-known results in literature. We give some examples to illustrate the usability of our results. Moreover, we prove the fixed point results in generalized metric space endowed with an arbitrary binary relation and the fixed point results in generalized metric space endowed with graph. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of (α, β)-(ψ, φ)-contractive mapping in b-metric spaces. We establish some fixed point theorems for such mappings and also give an example supporting our results. Finally, we apply our main results to prove a fixed point theorem involving a cyclic mapping. [ABSTRACT FROM AUTHOR]

In this work, we establish some fixed point theorems by revisiting the notion of ψ-contractive mapping in Menger PM-spaces. One of our results (namely, Theorem 2.3) may be viewed as a possible answer to the problem of existence of a fixed point for generalized type contractive mappings in M-complete Menger PM-spaces under arbitrary t-norm. Some examples are furnished to demonstrate the validity of the obtained results. [ABSTRACT FROM AUTHOR]