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In this paper, we focus on the existence of the best proximity points in binormed linear spaces. As a consequence, we obtain some fixed point results. We also provide some illustrations to support our claims. As applications, we obtain the existence of a solution to split feasible and variational inequality problems. [ABSTRACT FROM AUTHOR]

There are situations when we have to resort to the approximate optimal solution of equations of the type g(t) = t when g is not a self-map, because exact solution of that equation does not exist. The existence of such optimal solutions are ensured by best proximity point theorems. In this paper, we define multivalued Geraghty contraction (MVGC) in a complete metric space and establish the corresponding best proximity point (BPP) result. Our result extends the famous result due to Geraghty on fixed points. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a class of nonlinear operators-the class of general historydependent operators. These are the operators defined on spaces of functions endowed with a structure of Banach space (the case of bounded interval of time) or Frechet space (the case of unbounded interval of time). We state and prove various properties of such operators, including fixed point properties. Moreover, we also study several classes of differential equations in Banach spaces, for which we our previous results can be applied. [ABSTRACT FROM AUTHOR]

In this paper, we explain some sufficient conditions for unitariness of Toeplitz operators and little Hankel operators on the Bergman space. [ABSTRACT FROM AUTHOR]

In this paper, a one-to-one correspondence between Bessel sequences and bounded linear operators is provided. This leads to an algebra structure on the set of all Bessel sequences in a separable Hilbert space. Some kinds of frames as special classes of operators are considered. Also, normal Bessel sequences and positive frames are presented. Finally, power means of positive frames are introduced. These allow researches to construct a large number of new frames from existing frames. [ABSTRACT FROM AUTHOR]

In this paper, we show that the contractive definition considered by Proinov [Fixed point theorems in metric spaces, Nonlinear Analysis 64 (2006) 546 - 557] is strong enough to generate a fixed point but does not force the mapping to be continuous at the fixed point. Thus we provide several answers to the open question posed by B.E. Rhoades in Contractive definitions and continuity, Contemporary Mathematics 72(1988), 233-245. [ABSTRACT FROM AUTHOR]

In this paper, we extend relation-theoretic contraction principle due to Alam and Im- dad to a nonlinear contraction using a relatively weaker class of continuous control functions employing a locally finitely T -transitive binary relation, which improves the corresponding fixed point theorems especially due to: Alam and Imdad (J. Fixed Point Theory Appl. 17 (2015) 693-702), Agarwal et al: (Applicable Analysis, 87 (1) (2008) 109-116), Berzig and Karapinar (Fixed Point Theory Appl. 2013:205 (2013) 18 pp), Berzig et al: (Abstr. Appl. Anal. 2014:259768 (2014) 12 pp) and Turinici (The Sci. World J. 2014:169358 (2014) 10 pp). [ABSTRACT FROM AUTHOR]

In this paper we consider the Ln : A → A, Ln f(z) = (1 - λ) Dn f(z) + λIn f (z) linear operator, where Dn is the Sălăgean differential operator and I n is the Sălăgean integral operator. We study several differential subordinations generated by Ln. We introduce a class of holomorphic functions Lnm(β), and obtain some subordination results. [ABSTRACT FROM AUTHOR]

In this paper, we deal with the existence of the mild solutions to the fractional impulsive evolution equations. By definitions of the lower and upper quasi-solutions and technique of mixed monotone iterative, we get several existence results. The results are new and extend previously known results. An example illustrates the main results. [ABSTRACT FROM AUTHOR]

Let Mn be the algebra of all n × n matrices with entries in the field of real numbers. For a matrix Z ∊ Mn, it is said that a linear map T : Mn →Mn is multiplicative at Z if T (AB) = T (A)T (B) whenever AB = Z. In this paper we investigate some properties of multiplicative mapping at invertible matrices and also we characterize all multiplicative isomorphisms at invertible matrices. Then we give an example to show that multiplicativity at I doesn't imply multiplicativity on Mn, where I ∊ Mn is the identity matrix. [ABSTRACT FROM AUTHOR]

In this paper, using the concept of statistical A-summability which is stronger than classical convergence and A-statistical convergence, we obtain a Korovkin-type approximation theorem for double sequences of positive linear operators of two variables from Hw (K) to CB (K). Also, we give an example such that our new approximation result works but its classical and A-statistical cases do not work. [ABSTRACT FROM AUTHOR]

In this paper, we investigate a class of 2nth-order regular differential operator with eigenparameter-dependent boundary conditions and transmission conditions at an interior discontinuous point. By constructing a new linear operator A associated with the problem, we prove that the operator A is self-adjoint in a suitable Hilbert space H, and the eigenvalues of the problem coincide with those of A. In terms of basic solutions of differential equation, we show that the eigenvalues of this problem coincide with the zeros of the entire function det Φ(1, λ), and obtain that the operator A has only point spectrum. [ABSTRACT FROM AUTHOR]

In this paper, we use the notion of ideal to obtain two more general concepts and call them as I-A-statistical convergence and ideal A-summability. We also use the the concept of I-A-statistical convergence to prove a Korovkin type approximation theorem for double sequences of positive linear operators and present an interesting example to show that our Korovkin theorem is stronger than those proved earlier. [ABSTRACT FROM AUTHOR]

The paper is devoted to defining a new general class of linear and positive operators depending on a certain function φ. This new class of linear and positive operators generalizes the Szász-Mirakjan operators. For this new class of operators we establish a convergence theorem and the evaluation of the rate of convergence, in terms of the modulus of continuity. [ABSTRACT FROM AUTHOR]

In this paper, we study the statistical approximation properties of real and complex Post-Widder operators based on q-integers. We also obtain a Voronovskaya-type formula in statistical sense for these operators. [ABSTRACT FROM AUTHOR]

In this paper, we introduce q-Szász Schurer operators and calculate their moments. The transformation properties, Korovkin type approximation theorem and rate of convergence of the operators are studied. We further obtain global estimates for q??Szász Schurer operators in terms of some Lipschitz classes. [ABSTRACT FROM AUTHOR]

This study is the continuation of our former work [O. Duman and E. Erkusş, Comput. Math. Appl. 52 (2006) 967-974] in which we obtained a statistical Korovkin-type approximation theorem for a sequence of positive linear operators defined on the space of all real-valued continuous and 2π periodic functions on the real m-dimensional space. In this paper, we compute the statistical rates of this statistical approximation. [ABSTRACT FROM AUTHOR]

The aim of this paper is to present a class of linear positive operators of discrete type and its statistical approximation properties obtained by using a Bohman-Korovkin type theorem. [ABSTRACT FROM AUTHOR]