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Very recently, Pushpa and Vasuki (Arab. J. Math. 11, 355–378, 2022) have proved Eisenstein series identities of level 5 of weight 2 due to Ramanujan and some new Eisenstein identities for level 7 by the elementary way. In their paper, they introduced seven restricted color partition functions, namely P ∗ (n) , M (n) , T ∗ (n) , L (n) , K (n) , A (n) , and B(n), and proved a few congruence properties of these functions. The main aim of this paper is to obtain several new infinite families of congruences modulo 2 a · 5 ℓ for P ∗ (n) , modulo 2 3 for M(n) and T ∗ (n) , where a = 3 , 4 and ℓ ≥ 1 . For instance, we prove that for n ≥ 0 , P ∗ (5 ℓ (4 n + 3) + 5 ℓ - 1) ≡ 0 (mod 2 3 · 5 ℓ). In addition, we prove witness identities for the following congruences due to Pushpa and Vasuki: M (5 n + 4) ≡ 0 (mod 5) , T ∗ (5 n + 3) ≡ 0 (mod 5). [ABSTRACT FROM AUTHOR]

In the paper, we investigate the uniqueness problem of a meromorphic function and its difference operator to the most general setting via two shared set problems and thus improve a recent result of Chen–Chen (Bull Malays Math Sci Soc 35(3): 765-774, 2012). [ABSTRACT FROM AUTHOR]

Abstract Very recently, Pushpa and Vasuki (Arab. J. Math. 11, 355–378, 2022) have proved Eisenstein series identities of level 5 of weight 2 due to Ramanujan and some new Eisenstein identities for level 7 by the elementary way. In their paper, they introduced seven restricted color partition functions, namely $$P^{*}(n), M(n), T^{*}(n), L(n), K(n), A(n)$$ P ∗ ( n ) , M ( n ) , T ∗ ( n ) , L ( n ) , K ( n ) , A ( n ) , and B(n), and proved a few congruence properties of these functions. The main aim of this paper is to obtain several new infinite families of congruences modulo $$2^a\cdot 5^\ell $$ 2 a · 5 ℓ for $$P^{*}(n)$$ P ∗ ( n ) , modulo $$2^3$$ 2 3 for M(n) and $$T^*(n)$$ T ∗ ( n ) , where $$a=3, 4$$ a = 3 , 4 and $$\ell \ge 1$$ ℓ ≥ 1 . For instance, we prove that for $$n\ge 0$$ n ≥ 0 , $$\begin{aligned} P^{*}(5^\ell (4n+3)+5^\ell -1)&\equiv 0\pmod {2^3\cdot 5^{\ell }}. \end{aligned}$$ P ∗ ( 5 ℓ ( 4 n + 3 ) + 5 ℓ - 1 ) ≡ 0 ( mod 2 3 · 5 ℓ ) . In addition, we prove witness identities for the following congruences due to Pushpa and Vasuki: $$\begin{aligned} M(5n+4)\equiv 0\pmod {5},\quad T^{*}(5n+3)\equiv 0\pmod {5}. \end{aligned}$$ M ( 5 n + 4 ) ≡ 0 ( mod 5 ) , T ∗ ( 5 n + 3 ) ≡ 0 ( mod 5 ) .

We study the asymptotic behavior of trajectories of the continuous dynamical system(CDS) associated with the discrete viscosity approximation method for fixed point problem of nonexpansive mapping (DDS) which was introduced by Moudafi (J Math Anal Appl 241:46–55, 2000). We establish that the trajectories x(t) of the continuous dynamical system (CDS) has an asymptotic behavior similar to the behavior of the sequences (x n) generated by the discrete viscosity approximation (DDS) [ABSTRACT FROM AUTHOR]

Abstract This paper aims to study the existence and stability results concerning a fractional partial differential equation with variable exponent source functions. The local existence result for $$\alpha \in (0,1)$$ α ∈ ( 0 , 1 ) is established with the help of the $$\alpha $$ α -resolvent kernel and the Schauder-fixed point theorem. The non-continuation theorem is proved by the fixed point technique and accordingly the global existence of solution is achieved. The uniqueness of the solution is obtained using the contraction principle and the stability results are discussed by means of Ulam-Hyers and generalized Ulam-Hyers-Rassias stability concepts via the Picard operator. Examples are provided to illustrate the results.

Abstract The aim of this paper is twofold: first, we obtain various curvature inequalities which involve the Ricci and scalar curvatures of horizontal and vertical distributions of anti-invariant Riemannian submersion defined from conformal Kenmotsu space form onto a Riemannian manifold. Second, we obtain the Chen–Ricci inequality for the said Riemannian submersion. The equality cases of all the inequalities are studied. Moreover, these curvature inequalities are studied under two different cases: the structure vector field $$\xi $$ ξ being vertical or horizontal.

Abstract The aim of the present paper is to analyze sharp type inequalities including the scalar and Ricci curvatures of anti-invariant Riemannian submersions in Kenmotsu space forms $$K_{s}(\varepsilon )$$ K s ( ε ) . We give non-trivial examples for anti-invariant Riemannian submersions, investigate some curvature relations between the total space and fibres according to vertical and horizontal cases of $$\xi $$ ξ . Moreover, we acquire Chen-Ricci inequalities on the $$\ker \vartheta _{*}$$ ker ϑ ∗ and $$(\ker \vartheta _{*})^{\bot }$$ ( ker ϑ ∗ ) ⊥ distributions for anti-invariant Riemannian submersions from Kenmotsu space forms according to vertical and horizontal cases of $$\xi $$ ξ .