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Vol.23 No.2
Abstract
This paper shows that the solutions to the nonlinear perturbed differential system <TEX>$y{\prime}=f(t,y)+\int_{t_0}^{t}g(s,y(s),T_1y(s))ds+h(t,y(t),T_2y(t))$</TEX>, have the bounded property by imposing conditions on the perturbed part <TEX>$\int_{t_0}^{t}g(s,y(s),T_1y(s))ds,h(t,y(t),T_2y(t))$</TEX>, and on the fundamental matrix of the unperturbed system y′ = f(t, y) using the notion of h-stability.
Abstract
In this paper, we introduce the notions of soft L-fuzzy preproximities in complete residuated lattices. We prove the existence of initial soft L-fuzzy preproximities. From this fact, we define subspaces and product spaces for soft L-fuzzy preproximity spaces. Moreover, we give their examples.
Abstract
In this paper, we present some common fixed point theorems for two pairs of weakly compatible self-mappings on multiplicative metric spaces satisfying a generalized Meir-Keeler type contractive condition. The results obtained in this paper extend, improve and generalize some well known comparable results in literature.
Abstract
In this paper, we solve the quadratic ρ-functional inequalities (0.1) <TEX>${\parallel}f(x+y)+f(x-y)-2f(x)-2f(y){\parallel}$</TEX> <TEX>$\leq$</TEX> <TEX>${\parallel}{\rho}(4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y)){\parallel}$</TEX>, where <TEX>$\rho$</TEX> is a fixed complex number with <TEX>$\left|{\rho}\right|$</TEX> < 1, and (0.2) <TEX>${\parallel}4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y){\parallel}$</TEX> <TEX>$\leq$</TEX> <TEX>${\parallel}{\rho}(f(x+y)+f(x-y)-2f(x)-2f(y)){\parallel}$</TEX>, where ρ is a fixed complex number with |ρ| < <TEX>$\frac{1}{2}$</TEX>. Furthermore, we prove the Hyers-Ulam stability of the quadratic ρ-functional inequalities (0.1) and (0.2) in complex Banach spaces.
Abstract
In this paper, we solve the additive ρ-functional inequalities (0.1)<TEX>${\parallel}f(x+y)+f(x-y)-2f(x){\parallel}$</TEX> <TEX>$\leq$</TEX> <TEX>${\parallel}{\rho}(2f(\frac{x+y}{2})+f(x-y)-2f(x)){\parallel}$</TEX>, where ρ is a fixed complex number with |ρ| < 1, and (0.2) <TEX>${\parallel}2f(\frac{x+y}{2})+f(x-y)-2f(x)){\parallel}$</TEX> <TEX>$\leq$</TEX> <TEX>${\parallel}{\rho}f(x+y)+f(x-y)-2f(x){\parallel}$</TEX>, where ρ is a fixed complex number with |ρ| < 1. Furthermore, we prove the Hyers-Ulam stability of the additive ρ-functional inequalities (0.1) and (0.2) in complex Banach spaces.
Abstract
Let <TEX>$M_1f(x,y):=\frac{3}{4}f(x+y)-\frac{1}{4}f(-x-y)+\frac{1}{4}(x-y)+\frac{1}{4}f(y-x)-f(x)-f(y)$</TEX>, <TEX>$M_2f(x,y):=2f(\frac{x+y}{2})+f(\frac{x-y}{2})+f(\frac{y-x}{2})-f(x)-f(y)$</TEX> Using the direct method, we prove the Hyers-Ulam stability of the additive-quadratic ρ-functional inequalities (0.1) <TEX>$N(M_1f(x,y)-{\rho}M_2f(x,y),t){\geq}\frac{t}{t+{\varphi}(x,y)}$</TEX> and (0.2) <TEX>$N(M_2f(x,y)-{\rho}M_1f(x,y),t){\geq}\frac{t}{t+{\varphi}(x,y)}$</TEX> in fuzzy Banach spaces, where ρ is a fixed real number with ρ ≠ 1.
Abstract
In this paper we obtain some retarded integral inequalities involving Stieltjes derivatives and we use our results in the study of various qualitative properties of a certain retarded impulsive differential equation.
Abstract
After publication of the original article [1], the authors noticed the title was incorrect as follows: ‘Huge contraction on partially ordered metric spaces.’ The correct version of the title is below: Contraction on partially ordered metric spaces
Abstract
After publication of the original article [1], the authors noticed the title was incorrect as follows: ‘Huge coupled coincidence point theorem for generalized compatible pair of mappings with applications.’ The correct version of the title is below: Coupled coincidence point theorem for generalized compatible pair of mappings with application