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The paper is devoted to prove the existence of solutions for an infinite system of non- linear integral equations. This system is investigated in the WC-Banach algebra C(I; c0), the space of all continuous functions acting from an interval I into the sequence space c0. Making use of the measure of weak noncompactness and the weak topology, we establish some fixed point theorems for the sum and the product of nonlinear weakly sequentially continuous operat- ors acting onWC-Banach algebra involving w-contractive operators. [ABSTRACT FROM AUTHOR]

In this paper, we obtain some existence results for multivalued contraction mappings in the context of an O-complete orthogonal metric space (not necessarily complete metric space). Also, we provide a partial solution to Reich’s problem for multivalued orthogonal contraction mappings and extend Mizoguchi-Takahashi’s point theorem. In addition, we give an example to demonstrate the applicability of our established results. We study the solution of a differential equation and its Ulam’s stability as an application of the obtained results. [ABSTRACT FROM AUTHOR]

Inspired by the paper of Fazli and Nieto in [Open Math. 17 (2019) 499--512], we establish new existence and uniqueness result for a type of fractional Bagley--Torvik differential equation. Reported result not only generalizes previous results but also adopts different technique. We finish this study by concluding remarks which discuss the preference of our theorem compared to previous results. An example is constructed with specific parameters that requires weaker conditions for the existence of a unique solution. Meanwhile, we construct an iterative sequence that converges to the unique solution and can not be commented via the results of Fazli and Nieto. [ABSTRACT FROM AUTHOR]

In this paper, a new class of nonconvex nonsmooth multiobjective programming problems with both inequality and equality constraints defined in a real Banach space is considered. Under the nondifferentiable vectorial (Φρ)w-invexity notion introduced in the paper, optimality conditions and duality results in Mond-Weir sense are established for the considered nonsmooth vector optimization problem. It turns out that the results developed here under (Φρ)w-invexity are applicable for a larger class of nonconvex nondifferentiable multiobjective programming problems than under several generalized convexity notions existing in the literature. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce and study the concepts of statistical convergence and statistical summability for martingale sequences of random variables via deferred Cesaro ` mean. We then establish an inclusion theorem concerning the relation between these two beautiful and potentially useful concepts. Also, based upon our proposed notions, we state and prove new Korovkin-type approximation theorems with algebraic test functions for a martingale sequence over a Banach space. Moreover, we demonstrate that our theorems effectively extend and improve most (if not all) of the previously existing results (in statistical and classical versions). Finally, by using the generalized Bernstein polynomials, we present an illustrative example of a martingale sequence in order to demonstrate that our established theorems are stronger than their traditional and statistical versions. [ABSTRACT FROM AUTHOR]

Consider a simple connected graph G = (V(G),E(G)), where V(G) represents the vertex set and E(G) represents the edge set respectively. A subset W of V(G) is called a resolving set for a graph G if for every two distinct vertices x, y ∈V(G), there exist some vertex w ∈W such that d(x,w) 6= d(y,w), where d(u, v) denotes the distance between vertices u and v. A resolving set of minimal cardinality is called a metric basis for G and its cardinality is called the metric dimension of G, which is denoted by β(G). A subset D of V(G) is called a doubly resolving set of G if for every two distinct vertices x, y of G, there are two vertices u, v ∈ D such that d(u, x) - d(u, y) 6= d(v, x) - d(v, y). A doubly resolving set with minimum cardinality is called minimal doubly resolving set. This minimum cardinality is denoted by ψ(G). In this paper, we determine the minimal doubly resolving sets for antiprism graphs denoted by An with n ≥ 3 and for Mobius ladders denoted by Mn, for every even positive integer n ≥ 8. It has been proved that ψ(An) = 3 for n ≥ 3 and ψ(Mn) = ( 3, if n ≡ 0 or 4 (mod 8) 4, if n ≡ 2 or 6 (mod 8) for every even positive integer n ≥ 8. [ABSTRACT FROM AUTHOR]

Farthest point problem states that "Must every uniquely remotal set in a Banach space be singleton?" In this paper we introduce the notion of partial ideal statistical continuity of a function which is way weaker than continuity of a function. We give an example to show that partial ideal statistical continuity is weaker than continuity. In this paper we use Ideal summability to give some answers to FPP problem which improves the result in [13]. We prove that if E is a non-empty, bounded, uniquely remotal subset in a real Banach space X such that E has a Chebyshev center c and the farthest point map F : X → E restricted to [c, F(c)]? is partially ideal statistically continuous at c then E is singleton. [ABSTRACT FROM AUTHOR]

In the present paper, we introduce and study the concepts of statistical convergence and statistical summability for martingale difference sequences of random variables via deferred weighted summability mean. We then establish an inclusion theorem concerning the relation between these two beautiful concepts. Also, based upon our proposed notions, we state and prove new Korovkin-type approximation theorems with algebraic test functions for a martingale difference sequence over a Banach space and demonstrate that our theorems effectively extend and improves most (if not all) of the previously existing results (in statistical and classical versions). Finally, we present an illustrative example by using the generalized Bernstein polynomial of a martingale difference sequence in order to demonstrate that our established theorems are stronger than its traditional and statistical versions. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the concept of fuzzy barrels on locally convex fuzzy topological vector spaces. We present some characterizations of the fuzzy locally convex spaces, which are fuzzy barrelled. Using fuzzy barrels, we prove that the same fuzzy sets are bounded in any fuzzy topology of dual pair. Finally, we prove the Banach-Steinhaus theorem for the fuzzy topological vector spaces. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the finite approximate controllability of fractional semilinear differential equations involving the Hilfer derivative. We show that if the linear part is approximate controllable, then under suitable conditions the semilinear system is finite approximate controllable. [ABSTRACT FROM AUTHOR]

In this paper, we study to approximate solutions of quasi-equilibrium problems in Banach spaces, which generalizes equilibrium problems and quasi-variational inequalities. In fact, we prove weak convergence of the sequence generated by the proximal point method to a solution of the quasi-equilibrium problem. Then we show that the generated sequence converges strongly to a solution of the quasi-equilibrium problem. [ABSTRACT FROM AUTHOR]

In this paper, some existence results for generalized vector equilibrium-like problems (for short, GVELPs) are established by virtue of a generalized KKM-Fan theorem in topological vector spaces. In addition, some applications to vector optimization problems are also given. The results presented in this paper are the extension and improvement of the corresponding results of other authors. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study modified two-step iteration process for a pair of quasi-nonexpansive mapping and asymptotically quasi-nonexpansive mapping in the intermediate sense. We also establish some strong convergence theorems and a weak convergence theorem for this iteration scheme and mappings in the framework of real Banach spaces. The results presented in this paper extend, improve and generalize some previous results from the existing literature (see for example [1, 3, 5-7, 9-13]). [ABSTRACT FROM AUTHOR]

In this paper, we investigate the additive (α, β)-functional equation ... for all complex numbers α with [α] D 1 and for a fixed nonzero complex number β. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (α, β)-functional equation (0.1) in complex Banach spaces. [ABSTRACT FROM AUTHOR]

Recently, B. Samet et al. (Fixed Point Theory and Appl. 2013:5, 2013, doi:10.1186/1687-1812-2013-5) has introduced the concept of new contraction mappings and obtained results on the fixed point for nonlinear contractive mappings in a metric space. In the present paper, we introduce the concept of a new contraction via the measure of non-compactness on a Banach space, we obtain a few generalizations of Darbo fixed point theorem and extend some recent results of Aghajani et al. We also show the applicability of obtained results to the theory of integral equations. [ABSTRACT FROM AUTHOR]

In this paper, the exponential dichotomy, and Tikhonov and Banach fixed point theorems are used to study the existence and uniqueness of pseudo almost periodic solutions of nonhomogeneous iterative functional differential equations of the form x'(t)= λ1(t)x(t)+ λ 2(t)x[2](t)+...+λn(t)x[n](t)x[n](t)+f(t). [ABSTRACT FROM AUTHOR]

The purpose of this paper is to transpose some of the results regarding the coupled fixed point theory, developed by Bhaskar and Lakshmikantham [7], using the approaches of Ben-El-Mechaiekh [2], Asgari, Mousavi [1] and Berinde [3]. The first approach replaces the partial order relation from the Ran-Reurings fixed point theorem [10] with a transitive one, the second one uses a reflexive-only relation and whereas the third one introduces the tripled fixed points. Our aim is to obtain some generalized fixed point theorems, containing a more simple symmetrical condition, also extending them for the case of tripled fixed point. [ABSTRACT FROM AUTHOR]

In this paper we extend Darbo's fixed point theorem in Banach spaces and obtain a tripled fixed point theorem. The technique of measure of noncompactness is the main tool in carrying out our proof. Finally, as an application of our results, we analyze the existence of solutions for a system of neutral differential equations. [ABSTRACT FROM AUTHOR]

In this paper, we shall introduce the concepts of FG-contraction and ψG-contraction in uniform space endowed with graph to investigate the existence of a fixed point of mappings satisfying these notions. We shall also introduce a common fixed point theorem for pair of mappings satisfying the notion of ψG-contraction in uniform space endowed with graph. [ABSTRACT FROM AUTHOR]

In this paper, we prove a tripled common fixed point theorem of Suzuki type for a pair of hybrid mappings in metric spaces. Our result generalizes and modifies several comparable results in the literature. We also provide an example to support our theorem. [ABSTRACT FROM AUTHOR]

In this paper we investigate the generalized Hyers-Ulam stability of mappings of m-semigroups m ∊ N; m ≥ 2 into Banach spaces. For m = 3 the results can be found in Amyari and Moslehian [Approximate homomorphisms of ternary semigroups, Lett. Math. Phys. 77 (2006), 1-9] with the mention that they are true in the class of normal m-semigroups which is larger than the class of commutative m-semigroups. For m = 2 we find certain results of Hyers [On the stability of the linear functional equation, Proc. Nat. Acad. Sci. USA, 27 (1941), 222-224], Aoki [On the stability of the linear transformation in Banach spaces,J. Math. Soc. Japan, 2 (1950), 64-66], Rassias, Th. M. [On the stability of the linear mapping in Banach space, Proc. Amer. Math, Soc. 72 (1978), 297-300 ] and Rassias, J. M. [Solution of a Problem of Ulam, J. Approx. Theory Math. 57 (1989), 268-273]. In addition, we establish the superstability of m-ary homomorphims into Banach algebras endowed with multiplicative norms, generalizing the results of Szekelyhidi [On a theorem of Baker, Lawrence and Zorzitto, Proc. Amer. Math. Soc., 84 (1982), 95-96] and Amyari and Moslehian (2006). [ABSTRACT FROM AUTHOR]

In this paper, the convergence of Mann iterative process with errors for generalized Lipschitz ϕ-quasi-accretive operators is proved in uniformly smooth Banach spaces. Our results improve the corresponding results of Chidume et al.[2]. [ABSTRACT FROM AUTHOR]