Some fixed point theorems and common fixed point theorem in Logarithmic convex structure are proved.

Some fixed point theorems and common fixed point theorem in Logarithmic convex structure are proved.

We say a functional equation $(xi)$ is stable if any function $g$ satisfying the equation $(xi)$ approximately is near to true solution of $(xi)$. Using fixed point methods, we investigate approximately higher ternary derivations in Banach ternary algebras via the Cauchy functional equation$$f(lambda_1x + lambda_2y + lambda_3z) = lambda_1f(x) + lambda_2f(y) + lambda_3f(z).$$

This paper presents the following new definition which is a natural combination of the definition for asymptotically double equivalent, double statistically limit and double $lambda^2$-sequences. The double sequence $lambda^2 = (lambda_{m,n})$ of positive real numbers tending to infinity such that$$lambda_{m+1,n}leqlambda_{m,n} + 1, lambda_{m,n+1}leqlambda{m,n} + 1,$$$$lambda_{m,n} -lambda_{m+1,n }leqlambda_{m,n+1}lambda_{m+1,n+1}, lambda_{1,1} = 1,$$and$$I_{m,n}={(k,l) : m -lambda_{m,n }+ 1 leq k leq m, n -lambda_{m,n} + 1 leq l leq n.$$For double $lambda^2$-sequence; the two non-negative sequences $x = (x_{k,l})$ and $y = (y_{k,l})$ are said to be$lambda^2$-asymptotically double statistical equivalent of multiple $L$ provided that for every $varepsilon> 0$$$P - lim_{m,n}frac{1}{lambda_{m,n}}|{(k,l)in I_{m,n}:|frac{x_{k,l}}{y_{k,l}}-Lgeqvarepsilon}|=0$$(denoted by $xsim^{S_{lambda^2}^L } y$) and simply $lambda^2$-asymptotically double statistical equivalent if $L = 1$.

In this paper, we study the existence of solutions for fractional evolution equations with nonlocal conditions. These results are obtained using Banach contraction fixed point theorem. Other results are also presented using Krasnoselskii theorem.

In this paper, we introduce and study a new topology related to a self mapping on a nonempty set. Let $X$ be a nonempty set and let $f$ be a self mapping on $X$. Then the set of all invariant subsets of $X$ related to $f$, i.e. $tau_f := {Asubseteq X : f(A)subseteq A}subseteq mathcal{P}(X)$ is a topology on $X$. Among other things, we find the smallest open sets contains a point $xin X$. Moreover, we find the relations between $f$ and $tau_f$ . For instance, we find the conditions on $f$ to show that whenever $tau_f$ is $T_0, T_1$ or $T_2$.

In this paper we introduce a sequential block iterative method and its simultaneous version with optimal combination of weights (instead of convex combination) for solving convex feasibility problems. When the intersection of the given family of convex sets is nonempty, it is shown that any sequence generated by the given algorithms converges to a feasible point. Additionally for linear feasibility problems, we give equivalency of our algorithms with sequential and simultaneous block Kaczmarz methods explaining the optimal weights have been inherently used in Kaczmarz methods. In addition, a convergence result is presented for simultaneous block Kaczmarz for the case of inconsistent linear system of equations.

In this paper, we discuss the existence and uniqueness of fixed points for Banach and Kannan contractions defined on modular spaces endowed with a graph. We do not impose the $Delta_2$-condition or the Fatou property on the modular spaces to give generalizations of some recent results. The given results play as a modular version of metric fixed point results.

In a multi-secret sharing scheme, several secret values are distributed among a set of n participants. In 2000 Chien et al.'s proposed a $(t, n)$ multi-secret sharing scheme. Many storages and public values required in Chien's scheme. Motivated by these concerns, some new $(t, n)$ multi-secret sharing schemes are proposed in this paper based on the Lagrange interpolation formula for polynomials and cipher feedback mode (CFB), which are easier than Chien's scheme in the secret reconstruction and require fewer number of public values and storages than Chien's scheme. Also our schemes don't need any one-way function and any simultaneous equations.

In this paper, firstly, we obtain some inequalities which estimates complex polynomials on the circles. Then, we use these estimates and a Moebius transformation to obtain the dual of this estimates for the lines in upper half-plane. Finally, for an increasing weight $v$ on the upper half-plane with certain properties and holomorphic functions f on the upper half-plane we obtain an equivalent representation for weighted supremum norm.

A matrix has an ordinary inverse only if it is square, and even then only if it is nonsingular or, in other words, if its columns (or rows) are linearly independent. In recent years needs have been felt in numerous areas of applied mathematics for some kind of partial inverse of a matrix that is singular or even rectangular. In this paper, some results on the Quasi-commuting inverses, are given and the effect of them in solving the case of linear system of equations where the coefficient matrix is a singular matrix, is illustrated.

In this paper, an attempt is made to present an extension of Darbo's theorem, and its application to study the solvability of a functional integral equation of Volterra type.

In this paper, coupled fixed point results of Bhaskar-Lakshmikantham type [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis 65 (2006) 1379-1393] are extend, generalized, unify and improved by using monotone mappings instead mappings with mixed monotone property. Also, an example is given to support these improvements.

In this attempt we proved results on points of coincidence and common fixed points for three self mappings satisfying generalized contractive type conditions in cone metric spaces. Our results generalizes some previous known results in the literature (eg. [5], [6])

In this paper, we investigate the Hyers-Ulam stability for the system of additive, quadratic, cubic and quartic functional equations with constants coefficients in the sense of dectic mappings in non-Archimedean normed spaces.

The conditions under which, multilinear forms (the symmetric case and the non symmetric case), can be written as a product of linear forms, are considered. Also, we generalize a result due to S. Kurepa for 2n-functionals in a group G.