and Applied Analysis 3 If any solution x of 1.1 is either oscillatory, or satisfies the condition 1.7 , or admits the asymptotic representation x i c 1 sin t − α i εi t , i 0, 1, 2, 3 , 1.8 where c / 0 and α are constants, the continuous functions εi i 0, 1, 2, 3 vanish at infinity and ε0 satisfies the inequality cε0 t > 0 for large t, then we say that 1.1 has weak property A. For n 3, the resu...

We will present a fixed point method for the stability theorems of functional equations of Jensen type as given by S.-M. Jung [11] and Wang Jian [10].

Banach initiated the study of fixed points through iterative sequences, which appeared as a base for metric fixed point theory. Many authors continue this pattern of finding fixed points, see for eaxmple [1]-[29]. Samet . al et [1] introduced the ideas of  - -contractive and  -admissible mappings and got fixed points of the mappings through iterative sequence satisfying these ideas on comple...

We use the fixed point method to prove the probabilistic Hyers–Ulam and generalized Hyers–Ulam–Rassias stability for the nonlinear equation f (x) = Φ(x, f (η(x))) where the unknown is a mapping f from a nonempty set S to a probabilistic metric space (X ,F,TM) and Φ : S×X → X , η : S → X are two given functions. Mathematics subject classification (2000): 39B52, 39B82, 47H10, 54E70.

Let C be a closed convex subset of a complete metrizable topological vector space (X ,d) and T : C → C a mapping that satisfies d(Tx,Ty) ≤ ad(x, y) + bd(x,Tx) + cd(y,Ty) + ed(y,Tx) + f d(x,Ty) for all x, y ∈ C, where 0 < a < 1, b ≥ 0, c ≥ 0, e ≥ 0, f ≥ 0, and a+ b + c + e + f = 1. Then T has a unique fixed point. The above theorem, which is a generalization and an extension of the results of se...

We will apply a fixed point method for proving the Hyers–Ulam stability of the functional equation f(x+ y) = f(x)f(y) f(x)+f(y) .

Well-founded fixed points have been used in several areas of knowledge representation and reasoning and to give semantics to logic programs involving negation. They are an important ingredient of approximation fixed point theory. We study the logical properties of the (parametric) well-founded fixed point operation. We show that the operation satisfies several, but not all of the equational pro...

In this paper, we study boundary value problems for differential equations involving Caputo derivative of order α ∈ (2, 3) in Banach spaces. Some sufficient conditions for the existence and uniqueness of solutions are established by virtue of fractional calculus, a special singular type Gronwall inequality and fixed point method under some suitable conditions. Examples are given to illustrate t...

Using the fixed point method, we prove the generalized HyersUlam stability of the following cubic-quartic functional equation f(2x+ y) + f(2x− y) = 3f(x+ y) + f(−x− y) + 3f(x− y) + f(y − x) (0.1) + 18f(x) + 6f(−x)− 3f(y)− 3f(−y) in fuzzy Banach spaces.

In this paper, we prove the stability in random normed spaces via fixed point method for the functional equation f ⎛⎝ n ∑ j=1 xj ⎞⎠ + (n − 2) n ∑ j=1 f(xj) − ∑ 1≤i<j≤n f(xi + xj) = 0. Mathematics Subject Classification: 39B82, 46S50, 46S40