Jessen type functionals and exponential convexity

Abstract

In this paper, we introduce the extension of Jessen functional and investigate logarithmic and exponential convexity. We also give mean value theorems of Cauchy and Lagrange type. Several families of functions are also presented related to our main results.

Approximation of an Additive ϱ1,ϱ2-Random Operator Inequality

“…Recently, some authors have published some papers on stability of functional equations in several spaces by the direct method and the fixed point method, for example, Banach spaces [6][7][8], fuzzy Menger normed algebras [9], fuzzy normed spaces [10], non-Archimedean random Lie C * -algebras [11], non-Archimedean random normed spaces [12], random multinormed space [13], random lattice normed spaces, and random normed algebras [14,15]. In [16,17], the authors studied the stability problem for fractional equations.…”

“…almost everywhere for each u, v ∈ U, ω ∈ Ω, and t > 0. Suppose that T: Ω × U ⟶ V be a random operator satisfying T(ω, 0) � 0 and (15). erefore, there is a unique additive random operator S:…”

Approximation of derivations and the superstability in random Banach ∗-algebras

“…For more details, see [7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]. Definition 2.4 A random Banach * -algebra B is a random complex Banach algebra (B, μ, T, T ), together with an involution on B which is a mapping g → g * from B into B that satisfies (i) g * * = g for g ∈ B;…”

Ekeland’s Variational Principle and Minimization Takahashi’s Theorem in Generalized Metric Spaces

“…Then, there exists y ∈ Z such that f (y) ≤ f (x); d(x, y) ≤ 1 and f (z) > f (y) − d(y, z) for all y = z. Now, we study generalized metric spaces and their properties, for more details and application, we refer to [7,[14][15][16][17][18][19][20][21][22][23].…”