For positive invertible operators A on a Hilbert space H and a fixed unit vector x ∈ H, define the normalized determinant by ∆x(A) := exp <ln Ax, x>. In this paper we prove among others that, if 0 < mI ≤ A ≤ MI, then 1 ≤ K M m [1/2 - 1/M-m <|A-1/2 (m+M)I|x,x>] ≤ ∆x(A)/ m /M-<Ax,x> M-m M/ <Ax,x>-m M-m ≤ K M /m [1/2 + 1 M-m <|A-1/2 (m+M)I|x,x>] ≤ K M m, for x ∈ H, ∥x∥ = 1, where K(·) is Kantorovich's ratio.

Our main aim is to introduce Clairaut slant submersions in complex geometry. We give the notion of Clairaut slant submersions from almost Hermitian manifolds onto Riemannian manifold in this article. We obtain some basic results on discussed submersions. Furthermore, we provide some examples to explore the geometry of Clairaut slant submersions.

In this paper, we generalizes the notion of fundamentally nonexpansive mappings introduced in [Fixed Point Theory and Applications , 2014 (2014), Paper No. 76] to k-nonexpansive mappings. We investigate various properties associated with these mappings and demonstrate some existence and convergence results for k-nonexpansive mappings in the setting of Banach spaces.

The present study introduces the concepts of ideal convergence (I-convergence), ideal Cauchy (I-Cauchy) sequences, I *-convergence, and I *-Cauchy sequences in intuitionistic fuzzy metric spaces. It defines I-limit and I-cluster points as a sequence in these spaces. Afterward, it examines some of their basic properties. Lastly, the paper discusses whether phenomena should be further investigated.

In this paper, we derive some subordination and superordination results for the generalized "Srivastava-Attiya" fractional integral operator. Some interesting corollaries for this operator is also obtained.

A Kirchhoff equation type with memory term competing with a logarithmic source is considered. By using potential well theory, we obtained the global existence of solution for the initial data in a stability set created from Nehari Manifold and prove blow up results for initial data in the instability set.

In this paper, we establish some fixed point results for F⊥-weak contraction in orthogonal metric space and we give an application for the solution of second order differential equation.

In this work deals with the p-Laplacian wave equation with damping terms in a bounded domain. Under suitable conditions, we obtain a lower bounds for the blow up time. Our result extends the recent results obtained by Baghaei (2017) and Zhou (2015), for p > 2.

In this paper, we introduce and investigate a new subclass of bi-prestarlike functions defined in the open unit disk, associated with Chebyshev Polynomials. Furthermore, we find estimates of first two coefficients of functions in these classes, making use of the Chebyshev polynomials. Also, we obtain the Fekete-Szegö inequalities for function in these classes. Several consequences of the results are also pointed out as corollaries.

In this work, taking into account the theta-function, we present a general class of multivalued weakly Picard operators on complete metric space. We also provide an example showing that it includes some earlier classes as properly.