In 1940 and 1964, Ulam proposed the general problem: “When is it true that by changing a little the hypotheses of a theorem one can still assert that the thesis of the theorem remains true or approximately true?”. In 1941, Hyers solved this stability problem for linear mappings. According to Gruber 1978 this kind of stability problems are of the particular interest in probability theory and in ...

Abstract In this paper, we investigate the existence and uniqueness of a solution for class ψ -Hilfer implicit fractional integro-differential equations with mixed nonlocal conditions. The arguments are based on Banach’s, Schaefer’s, Krasnosellskii’s fixed point theorems. Further, applying techniques nonlinear functional analysis, establish various kinds Ulam stability results analyzed problem,...

‎in this paper‎, ‎using fixed point method‎, ‎we prove the generalized hyers-ulam stability of‎ ‎random homomorphisms in random $c^*$-algebras and random lie $c^*$-algebras‎ ‎and of derivations on non-archimedean random c$^*$-algebras and non-archimedean random lie c$^*$-algebras for‎ ‎the following $m$-variable additive functional equation:‎ ‎$$sum_{i=1}^m f(x_i)=frac{1}{2m}left[sum_{i=1}^mfle...

In this paper, the authors investigate the generalized Hyers-UlamAoki-Rassias stability of a quartic functional equation g(2x+ y + z) + g(2x+ y − z) + g(2x− y + z) + g(−2x+ y + z) + 16g(y) + 16g(z) = 8[g(x+ y) + g(x− y) + g(x+ z) + g(x− z)] + 2[g(y + z) + g(y − z)] + 32g(x). (1) The above equation (1) is modified and its Hyers-Ulam-Aoki-Rassias stability for the following quartic functional equ...

Abstract A thermostat model described by a second-order fractional difference equation is proposed in this paper with one sensor and two sensors boundary conditions depending on positive parameters using the Lipschitz-type inequality. By means of well-known contraction mapping Brouwer fixed-point theorem, we provide new results existence uniqueness solutions. In work use Caputo operator Hyer–Ul...

this paper is an investigation of $l$-dual frames with respect to a function-valued inner product, the so called $l$-bracket product on $l^{2}(g)$, where g is a locally compact abelian group with a uniform lattice $l$. we show that several well known theorems for dual frames and dual riesz bases in a hilbert space remain valid for $l$-dual frames and $l$-dual riesz bases in $l^{2}(g)$.

The stability problem of functional equations was originated from a question of Ulam [66] concerning the stability of group homomorphisms: Let (G1, .) be a group and let (G2, ∗) be a metric group with the metric d(., .). Given ε > 0, does there exist a δ > 0, such that if a mapping h : G1 → G2 satisfies the inequality d(h(x1.x2), h(x1) ∗ h(x2)) < δ for all x1, x2 ∈ G1, then there exists a homom...

An elastic beam equation (EBEq) described by a fourth-order fractional difference is proposed in this work with three-point boundary conditions involving the Riemann–Liouville operator. New sufficient ensuring solutions’ existence and uniqueness of problem are established. The findings obtained employing properties discrete equations, Banach contraction, Brouwer fixed-point theorems. Further, w...