Approximation of an Additive ( 9 1 , 9 2 )-Random Operator Inequality

(1) where ρ1 and ρ2 are fixed nonzero complex numbers with � 2 √ |ρ1| + |ρ2|< 1. Next, he proved the Hyers–Ulam stability of the additive (ρ1, ρ2)-functional inequality (1) in Banach spaces. In this paper, we get a generalization from Park’s results [1] in MB-spaces. Let (Ω,U, μ) be a probability measure space. Assume that (U,BU) and (V,BV) are Borel measureable spaces, in which U and V are MB-spaces and T: Ω × U2⟶ V is a random operator. In MB-spaces, first we solve the additive (91, 92)-random operator inequality:

[1]  Janusz Brzdęk,et al.  A fixed point theorem in n-Banach spaces and Ulam stability , 2019, Journal of Mathematical Analysis and Applications.

[2]  Choonkill Park,et al.  Approximation of derivations and the superstability in random Banach ∗-algebras , 2018, Advances in Difference Equations.

[3]  T. F. Ibrahim,et al.  Stability of a fractional difference equation of high order , 2018, Journal of Nonlinear Sciences and Applications.

[4]  Yali Ding.  Ulam-Hyers stability of fractional impulsive differential equations , 2018, Journal of Nonlinear Sciences and Applications.

[5]  Themistocles M. Rassias,et al.  Superstability of Kannappan's and Van vleck's functional equations , 2018 .

[6]  Choonkill Park.  Bi-additive s-Functional Inequalities and Quasi-$$*$$∗-Multipliers on Banach Algebras , 2018, Rocky Mountain Journal of Mathematics.

[7]  R. Saadati,et al.  Nonlinear Stability of ρ-Functional Equations in Latticetic Random Banach Lattice Spaces , 2018 .

[8]  Soon-Mo Jung,et al.  A Fixed Point Approach to the Stability of a Mean Value Type Functional Equation , 2017 .

[9]  R. Agarwal,et al.  Approximation of the multiplicatives on random multi-normed space , 2017, Journal of inequalities and applications.

[10]  Rishi Naeem,et al.  Jessen type functionals and exponential convexity , 2017 .

[11]  Muhammad Arshad,et al.  Fixed point results for multivalued mappings on a sequence in a closed ball with applications , 2017 .

[12]  P. Kumam,et al.  Generalization of Khan fixed point theorem , 2017 .

[13]  Flavius Pater,et al.  On fuzzy normed algebras , 2016 .

[14]  Choonkill Park,et al.  Stability of cubic and quartic rho-functional inequalities in fuzzy normed spaces , 2016 .

[15]  Jürg Rätz,et al.  On the functional equation x + f (y + f(x)) = y + f (x + f(y)), II , 2015 .

[16]  P. Gǎvruţa,et al.  On the stability of an affine functional equation , 2013 .

[17]  Alireza Kamel Mirmostafaee,et al.  Perturbation of generalized derivations in fuzzy Menger normed algebras , 2012, Fuzzy Sets Syst..

[18]  Wlodzimierz Fechner,et al.  Stability of a composite functional equation related to idempotent mappings , 2011, J. Approx. Theory.

[19]  Endre Pap,et al.  Fixed Point Theory in Probabilistic Metric Spaces , 2001 .

[20]  Choonkill Park.  The stability of an additive (ρ_1, ρ_2)-functional inequality in Banach spaces , 2019, Journal of Mathematical Inequalities.

[21]  Jung Rye Lee,et al.  Additive s-functional inequality and hom-derivations in Banach algebras , 2019, Journal of Fixed Point Theory and Applications.

[22]  George Isac,et al.  Stability of ψ-additive mappings: applications to nonlinear analysis , 1996 .