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In mathematical physics, a direct problem is a problem of modeling some physical fields, processes, or phenomena, especially using partial differential equations (PDEs). The aim of solving a direct problem…
Echocardiography is a procedure that has been used in the critical care setting for a long time. Several working groups from different societies have published guidelines and consensus documents suggesting…
In this chapter, an integral-type contraction condition is used to establish some common fuzzy FPs of FS-valued mappings involving Θ-contractions in a MS. Theorem 3.1 Let ((Upsilon , d)) be…
To prove our first existence result for multivalued problem (1.1), we need the following known results. Lemma 3.1 ([30]) Let X be a Banach space. Let (F : [a, b]…
Frontiers | Integral bridge abutments in response to seasonal temperature changes: State of knowledge…
In this section we shall prove some common coupled fixed point theorems for different contractive mappings in the setting of (mathscr{C}^{star})-algebra-valued partial b-metric spaces. Now we give our main results.…
Since the explicit analytic formula of (V(t,s_{1},s_{2})) in Theorem 1 is expressed by two free boundaries (xi _{mathrm{low}}) and (xi _{mathrm{up}}), we need to solve the coupled integral equations of…
Some essentials from diamond calculus A time scale (mathbb{T}) is a nonempty closed subset of (mathbb{R}). It may be connected or not. Keeping the time scale discontinuity under consideration, the…
To prove Theorem 1.11, we first give some notations and lemmas. Let (f in L_{mathrm{loc}}^{1}(mu )), the sharp maximal operator is defined as follows $$ M^{sharp }f(x)=sup_{Bni x}frac{1}{mu (6B)} int…
We begin this part with the following definitions: Definition 3.1 Let (H:Omega ^{4}rightarrow Omega ) and (h:Omega rightarrow Omega ) be mappings defined on a metric space ((Omega ,omega )).…