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In this paper, we prove some existence and uniqueness results for some classes of deformable implicit fractional differential equations in b-Metric spaces with initial conditions. We base our arguments on some some fixed point theorems. Finally, we provide an example to illustrate our results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a new inertial type algorithm with self -- adaptive step -- size technique for approximating a common element of the set of solutions of pseudomonotone variational inequality problem and the set of common fixed point of a finite family of generic generalized nonspreading mappings in uniformly smooth and 2 -- uniformly convex real Banach space. Furthermore, we prove a strong convergence theorem of our algorithm without prior knowledge of the Lipschitz constant of the operator under some mild assumptions. We also give numerical examples to illustrate the performance of our algorithm. Our result generalize and improve many existing results in the literature. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of F--G--contraction mappings in F-metric spaces endowed with a graph and give some fixed point results for such contractions. Our results are generalization of some famous theorem in metric spaces to F--metric spaces endowed with a graph. Also, we give some examples that support obtained theoretical results. [ABSTRACT FROM AUTHOR]

In this paper, we will investigate the existence of some solutions for a multi singular fractional differential system with some boundary conditions. [ABSTRACT FROM AUTHOR]

In this paper, we study the existence of nontrivial solutions for a fractional boundary value problem in Hölder spaces by a technical approach based on Leray-Schauder nonlinear alternative. Moreover, using the concept of orthogonal set on Banach fixed point theorem we obtain another existence result with weaker conditions. Also, recent results are extended and improved. In addition, we give some examples to illustrate the feasibility and effectiveness of our results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of extended partial metric space and we present some fixed point theorems in generalized partial metric spaces involving linear and nonlinear contractions. [ABSTRACT FROM AUTHOR]

In this paper, firstly, we introduce a new extension of F-Suzuki-contraction mappings namely generalized Fp-Suzuki contraction. Moreover, we prove a fixed point theorem for such contraction mappings even without considering the completeness condition of space. In the following, we respond the open question of Rhoades(see Rhoades [26], p.242) regarding existence of a contractive definition which is strong enough to generate a fixed point but dose not force the mapping to be continuous at the fixed point. Also, we provide some examples show that our main theorem is a generalization of previous results. Finally, we give an application to the boundary value problem of a nonlinear fractional differential equation for our results. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the notion of dislocated Sb-metric space and describe some fixed point theorems concerning F-contraction in the setup of such spaces. We provide some examples to verify the effectiveness and applicability of our main results. [ABSTRACT FROM AUTHOR]

In this paper, we use the concept of a generalized - Geraghty contraction type mapping to introduce the new notion of - Geraghty type F-contraction multivalued mapping and prove some new common fixed point results for such contraction in b-metric-like spaces. Also, we give some examples to illustrate our main results, we also discuss existence a solution for a system of non-linear integral equation. [ABSTRACT FROM AUTHOR]

In this paper, we define a generalized c-distance in tvs-cone b-metric spaces and introduce some results about its properties. Then we prove some new fixed point and common fixed point results (with the underlying cone which is not normal). Respective results concerning mappings without periodic points are also deduced. Some examples are presented to validate our obtained results. An application to system of Fredholm integral equations is presented. [ABSTRACT FROM AUTHOR]

In this paper, we show that the relative algebraic interior is a suitable replacement for both of the topological interior and the algebraic interior for the cases where these are empty. Also, we present some properties of (relative) algebraic interior and some fixed point theorems for increasing mapping. The obtained results can be viewed as an extension and improvement of the known corresponding results. Also, some examples are to support our conclusions considered. [ABSTRACT FROM AUTHOR]

In this paper we present some fixed point theorems for mappings satisfying contractive conditions on C*-algebra-valued b-metric spaces. Specifically we extend some fixed point results on metric spaces to C*-algebra valued case and prove the related fixed point theorems. Also several theorems in existence of n-periodic points are given. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish the structure of C*- algebra-valued b2-metric space and give some fixed point theorems for self-maps with contractive or expansive conditions on such spaces. As an application we investigate existence and uniqueness solution for a type of integral equation. [ABSTRACT FROM AUTHOR]

The concept of a w-distance on a metric space has been introduced by Kada et al. [22]. They generalized Caristi fixed point theorem, Ekeland variational principle and the nonconvex minimization theorem according to Takahashi. In the present paper, we first introduce the notion of quasi w-distances in quasi-metric spaces, and then we will prove some fixed point theorems for L-contractive mappings in the class of quasi-metric spaces with w-distances via a control function introduced by Jleli and Samet [20]. These results generalize many fixed point theorems by Kada et al. [22], Suzuki [33], Ciric [15], Aydi et al. [6], Abbas and Rhoades [1], Kannan [23], Hicks and Rhoades [19], Du [16], Lakzian et al. [26], Lakzian and Rhoades [30] and others. Finally, some examples in support of the concepts and presented results are given. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present some new couple fixed point theorems for multivalued mappings which satisfy generalized weak contraction in ordered metric spaces. The results of this paper are generalizations of the main results of [3, 5, 9]. As an application, we show existence and uniqueness of solutions of a class of nonlinear integral equations. [ABSTRACT FROM AUTHOR]

We investigate the existence and uniqueness of the solution and also the rate of convergence of a numerical method for a fractional differential equation in both q-calculus and (p; q)-calculus versions. We use the Banach and Schauder fixed point theorems in this study. We provide two examples, one by definition of the q-derivative and the other by (p; q)-derivative. We compare the rate of convergence of the numerical method. We like to clear some facts on (p; q)-calculus. The data from our numerical calculations show well that q-calculus works better than (p; q)-calculus in each case. [ABSTRACT FROM AUTHOR]

In this work, we discuss the existence of solutions of infinite systems for a boundary value problem of Caputo fractional differential inclusions involving convex-compact multivalued maps. Our results are based on an appropriate fixed point theorem for condensing maps in the multivalued case. Eventually, we demonstrate an example to show the effectiveness and usefulness of the obtained result. [ABSTRACT FROM AUTHOR]

The notion of dualistic Geraghty Contraction is introduced. A new fixed point theorem is proved in the settings of complete dualistic partial metric spaces. The counterpart theorem provided in partial metric spaces is retrieved as a particular case of our new results. We give example to prove that the contractive conditions in the statement of our new fixed point theorem can not be replaced by those contractive conditions in the statement of the partial metric counterpart fixed point theorem. Moreover, we give an application of our fixed point theorem to show the existence of solution of integral equations. [ABSTRACT FROM AUTHOR]