Case (i): Let ϕ satisfy the Equation (32) under the orthogonality conditions (44).
In order to prove the case (i), let f be a C 0 strictly increasing solution with fixed points.
(a) In case (i), let | f ( p, q ) − g ( p, q ) | ≤ M for all p, q ∈ S and some constant M. Then either g is bounded or h satisfies ( C D M ).
In case (i), let | f ( p, q ) − g ( p, q ) | ≤ M for all p, q ∈ S and some constant M. Then either g is bounded or h satisfies ( C D M ).
Case-I: Let (x, y in [0, frac{4}{5} )), then we have vert Tx-Tyvert = 0 leqfrac{1}{3} bigl[vert x-yvert +vert Tx-yvert +vert x-Tyvert bigr], (x, y in [0, frac{4}{5} )). Case-II: Let (x, y in [frac{4}{5}, 1 ]), then vert Tx-Tyvert =bigglvert frac{x}{2}-frac{y}{2}biggrvert.
To verify that T is a Suzuki generalized nonexpansive mapping, consider the following cases: Case I: Let (xin [ 0,frac{1}{10} ) ), then (frac{1}{2}d(x,Tx)=frac{1-2x}{2} in ( frac{2}{5},frac {1}{2} ] ).
For the eigenvalues (mu _{1},; mu _{2}ne ;0) of nonsingular matrix C. We consider two special cases: Case I Let begin{aligned} C=left[ begin{array}{cc} {mu _{1} } & {0} {0} & {mu _{2} } end{array}right], end{aligned}then, in this case we are looking for a diagonal matrix begin{aligned} B=left[ begin{array}{cc} {b_{1} } & {0} {0} & {b_{2} } end{array}right], end{aligned}so that (E_{alpha } (B =C).
Usually I would be turned off by such a blatant rip off and lack of originality, but in this case I let it slide cus I love the old Burial sound so much".
Then the following cases occur: (i) Let d<1+2b.
